A381825 Odd cubefull exponentially odd numbers: numbers whose prime factorization has only odd primes and odd exponents that are larger than 1 (except for 1 whose prime factorization is empty).

1, 27, 125, 243, 343, 1331, 2187, 2197, 3125, 3375, 4913, 6859, 9261, 12167, 16807, 19683, 24389, 29791, 30375, 35937, 42875, 50653, 59319, 68921, 78125, 79507, 83349, 84375, 103823, 132651, 148877, 161051, 166375, 177147, 185193, 205379, 226981, 273375, 274625

Offset: 1

Author

Amiram Eldar, Mar 08 2025

Keywords

• nonn
• easy

Comments

Differs from its subsequence A369118 by having the terms 1, 19683 = 3^9, 1953125 = 5^9, 2460375 = 3^9 * 5^3, 6751269 = 3^9 * 7^3, 14348907 = 3^15, ... .

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A005408 and A335988.

Intersection A036966 and A376218.

Subsequence of A381824.

A369118 is a subsequence.

Cf. A065487.

Programs

Mathematica

Join[{1}, Select[Range[3, 300000, 2], AllTrue[FactorInteger[#][[;;, 2]],  #1 > 1 && OddQ[#1] &] &]]

PARI

isok(k) = k == 1 || (k % 2 && #select(x -> (x == 1) || !(x % 2), factor(k)[, 2]) == 0);

Formula

Sum_{n>=1} 1/a(n) = Product_{prime p >= 3} (1 + 1/(p*(p^2-1))) = (6/7) * A065487 = 1.05539241333308876809... .