Divisor functions · 58 sequences
The sequences of the family “divisor functions”, by A-number, with the share of their decomposable terms in the level class (k > L).
- primes · 1717
- polynomial · 1232
- quadratic form · 430
- prime values · 423
- residue class · 357
- digit rule · 306
- multiplicative · 199
- Beatty · 86
- divisor functions · 58
- binary rule · 48
- self-referential · 35
- complement · 23
- powers · 22
- summatory · 21
- arithmetic progression · 10
- smooth · 10
- forced divisor · 9
- sieve · 8
- block · 5
- base case · 1
| A-number | Name | Level |
|---|---|---|
| A001838 | Numbers k such that phi(k+2) = phi(k) + 2 | 44.8 % |
| A002202 | Values taken by totient function phi(m) (A000010) | 12.6 % |
| A003277 | Cyclic numbers: k such that k and phi(k) are relatively prime; also k such that there is just one group of order k, i.e., A000001(k) = 1 | 15.1 % |
| A003601 | Numbers j such that the average of the divisors of j is an integer: sigma_0(j) divides sigma_1(j). Alternatively, numbers j such that tau(j) (A000005(j)) divides sigma(j) (A000203(j)) | 11.9 % |
| A005100 | Deficient numbers: numbers k such that sigma(k) < 2k | 7.8 % |
| A005101 | Abundant numbers (sum of divisors of m exceeds 2m) | 14.9 % |
| A005153 | Practical numbers: positive integers m such that every k <= sigma(m) is a sum of distinct divisors of m. Also called panarithmic numbers | 17.5 % |
| A005237 | Numbers k such that k and k+1 have the same number of divisors | 21.9 % |
| A005277 | Nontotients: even numbers k such that phi(m) = k has no solution | 10.7 % |
| A005279 | Numbers having divisors d, e with d < e < 2*d | 15.2 % |
| A005598 | a(n) = 1 + Sum_{i=1..n} (n-i+1)*phi(i) | 100.0 % |
| A006532 | Numbers whose sum of divisors is a square | 45.4 % |
| A007617 | Values not in range of Euler phi function | 11.1 % |
| A023197 | Numbers k such that sigma(k) >= 3*k | 16.8 % |
| A028983 | Numbers whose sum of divisors is even | 9.6 % |
| A030513 | Numbers with 4 divisors | 15.7 % |
| A030515 | Numbers with exactly 6 divisors | 27.4 % |
| A030626 | Numbers with exactly 8 divisors | 16.5 % |
| A030628 | 1 together with numbers of the form p*q^4 and p^9, where p and q are distinct primes | 29.8 % |
| A030630 | Numbers with 12 divisors | 21.3 % |
| A030634 | Numbers with 16 divisors | 19.9 % |
| A030638 | Numbers with 20 divisors | 25.9 % |
| A034683 | Unitary abundant numbers: numbers k such that usigma(k) > 2*k | 14.6 % |
| A036433 | Number of divisors is a digit in the base 10 representation of n | 12.9 % |
| A036455 | Numbers n such that d(d(n)) is an odd prime, where d(k) is the number of divisors of k | 14.2 % |
| A036537 | Numbers whose number of divisors is a power of 2 | 10.2 % |
| A039770 | Numbers k such that phi(k) is a perfect square | 41.3 % |
| A045746 | Numbers whose sum of divisors is a triangular number | 63.0 % |
| A046642 | Numbers k such that k and number of divisors d(k) are relatively prime | 16.7 % |
| A048109 | Numbers having equally many squarefree and nonsquarefree divisors; number of unitary divisors of n (A034444) = number of non-unitary divisors of n (A048105) | 21.5 % |
| A053224 | Numbers k for which sigma(k) < sigma(k+1) | 16.0 % |
| A053868 | Numbers whose sum of proper divisors is odd | 17.9 % |
| A054741 | Numbers m such that totient(m) < cototient(m) | 10.2 % |
| A055638 | Numbers k for which sigma(k^2) is prime | 50.4 % |
| A059269 | Numbers m for which the number of divisors, tau(m), is divisible by 3 | 16.9 % |
| A062634 | Numbers k such that every divisor of k contains the digit 1 | 23.2 % |
| A065496 | Numbers n such that sigma(n) is a nontrivial power, i.e., sigma(n) = a^b where a and b are greater than 1 | 44.3 % |
| A069059 | Numbers k such that k and sigma(k) are not relatively prime | 12.6 % |
| A071395 | Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers) | 53.8 % |
| A074627 | Numbers n such that sigma(n) is divisible by 6 | 9.2 % |
| A087248 | Squarefree abundant numbers | 15.0 % |
| A088723 | Numbers k with at least one divisor d>1 such that d+1 also divides k | 14.5 % |
| A091191 | Primitive abundant numbers: abundant numbers (A005101) having no abundant proper divisor | 25.3 % |
| A111592 | Admirable numbers. A number n is admirable if there exists a proper divisor d' of n such that sigma(n)-2d'=2n, where sigma(n) is the sum of all divisors of n | 24.8 % |
| A112886 | Positive integers that have no triangular divisors > 1 | 2.3 % |
| A113502 | A number n is included if at least one of its divisors > 1 is a triangular number (i.e., is of the form m(m+1)/2, m >= 2) | 14.5 % |
| A123193 | Natural numbers with number of divisors equal to a Fibonacci number | 14.0 % |
| A145749 | Numbers n such that sigma(n)+phi(n)=sigma(n+1)+phi(n+1) | 47.3 % |
| A162527 | Numbers k whose largest divisor <= sqrt(k) equals 7 | 23.1 % |
| A174905 | Numbers with no pair (d,e) of divisors such that d < e < 2*d | 8.6 % |
| A175495 | Positive integers k such that k < 2^d(k), where d(k) is the number of divisors of k | 16.6 % |
| A179188 | Numbers n such that phi(n) = phi(n+6), with Euler's totient function phi=A000010 | 38.0 % |
| A217139 | Numbers n such that phi(n) = phi(n+12), with Euler's totient function phi = A000010 | 38.2 % |
| A230577 | Positive integers that have exactly 6 odd divisors | 24.9 % |
| A236562 | Numbers n such that A049820(x) = n has a solution | 11.9 % |
| A257219 | Numbers that have at least one divisor containing the digit 2 in base 10 | 10.6 % |
| A257220 | Numbers that have at least one divisor containing the digit 3 in base 10 | 11.3 % |
| A274357 | Numbers n such that n and n+1 both have 8 divisors | 24.7 % |