Summatory · 21 sequences
The sequences of the family “summatory”, 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 |
|---|---|---|
| A000788 | Total number of 1's in binary expansions of 0, ..., n | 24.1 % |
| A001768 | Sorting numbers: number of comparisons for merge insertion sort of n elements | 28.3 % |
| A001855 | Sorting numbers: maximal number of comparisons for sorting n elements by binary insertion | 32.0 % |
| A002088 | Sum of totient function: a(n) = Sum_{k=1..n} phi(k), cf. A000010 | 87.3 % |
| A002815 | a(n) = n + Sum_{k=1..n} pi(k), where pi() = A000720 | 70.2 % |
| A005187 | a(n) = a(floor(n/2)) + n; also denominators in expansion of 1/sqrt(1-x) are 2^a(n); also 2n - number of 1's in binary expansion of 2n | 12.5 % |
| A006046 | Total number of odd entries in first n rows of Pascal's triangle: a(0) = 0, a(1) = 1, a(2k) = 3*a(k), a(2k+1) = 2*a(k) + a(k+1). a(n) = Sum_{i=0..n-1} 2^wt(i) | 55.2 % |
| A006218 | a(n) = Sum_{k=1..n} floor(n/k); also Sum_{k=1..n} d(k), where d = number of divisors (A000005); also number of solutions to x*y = z with 1 <= x,y,z <= n | 23.4 % |
| A007504 | Sum of the first n primes | 100.0 % |
| A013939 | Partial sums of sequence A001221 (number of distinct primes dividing n) | 15.3 % |
| A015614 | a(n) = -1 + Sum_{i=1..n} phi(i) | 93.3 % |
| A018805 | Number of elements in the set {(x,y): 1 <= x,y <= n, gcd(x,y)=1} | 98.0 % |
| A022559 | Sum of exponents in prime-power factorization of n! | 16.6 % |
| A024916 | a(n) = Sum_{k=1..n} k*floor(n/k); also Sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n (A000203) | 100.0 % |
| A034705 | Numbers that are sums of consecutive squares | 38.5 % |
| A037123 | a(n) = a(n-1) + sum of digits of n | 28.3 % |
| A046992 | a(n) = Sum_{k=1..n} pi(k) (cf. A000720) | 70.3 % |
| A051677 | Tetrahedron-tree numbers: a(n)=sum(b(m),m=1..n), b(m)=1, 1,3, 1,3,6, 1,3,6,10,..., 1,2,...,i*(i+1)2 | 69.4 % |
| A054353 | Partial sums of Kolakoski sequence A000002 | 11.8 % |
| A064608 | Partial sums of A034444: sum of number of unitary divisors from 1 to n | 26.4 % |
| A074741 | Sum of squares of gaps between consecutive primes | 43.0 % |