Powers · 22 sequences
The sequences of the family “powers”, 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 |
|---|---|---|
| A000961 | Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1) | 23.0 % |
| A001248 | Squares of primes | 100.0 % |
| A001597 | Perfect powers: m^k where m > 0 and k >= 2 | 99.3 % |
| A003485 | Hurwitz-Radon function at powers of 2 | 4.5 % |
| A007916 | Numbers that are not perfect powers | 9.7 % |
| A014439 | Differences between two positive cubes in exactly 1 way | 44.3 % |
| A015911 | Numbers k such that 2^k mod k is odd | 24.4 % |
| A022549 | Sum of a square and a nonnegative cube | 24.8 % |
| A024974 | Numbers that are the sum of 3 distinct positive cubes in 2 or more ways | 34.7 % |
| A024975 | Sums of three distinct positive cubes | 22.4 % |
| A025475 | 1 and the prime powers p^m where m >= 2, thus excluding the primes | 100.0 % |
| A045542 | Sub-perfect powers: perfect powers (squares, cubes etc., not including 1) minus 1 | 99.3 % |
| A053696 | Numbers that can be represented as a string of three or more 1's in a base >= 2 | 99.4 % |
| A054402 | Numbers that are the sum of a positive square and a positive cube in more than one way | 46.0 % |
| A055393 | Sum of a square and a nonnegative cube in more than one way | 45.8 % |
| A072774 | Powers of squarefree numbers | 10.7 % |
| A075109 | Odd perfect powers (1 together with numbers m^k, m odd, k >= 2) | 99.7 % |
| A080075 | Proth numbers: of the form k*2^m + 1 for k odd, m >= 1 and 2^m > k | 100.0 % |
| A106564 | Perfect squares which are not the difference of two primes | 100.0 % |
| A136773 | n! never ends in this many 0's in base 13 | 25.9 % |
| A195943 | Zeroless prime powers: Intersection of A000961 and A052382 | 23.6 % |
| A213382 | Numbers n such that n^n mod (n + 2) = n | 41.4 % |