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

1,2

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Intersection of A005408 and A335988.

Intersection A036966 and A376218.

Subsequence of A381824.

A369118 is a subsequence.

Cf. A065487.

Sequence in context: A137800 A125497 A179145 * A369118 A118092 A371189

Adjacent sequences: A381822 A381823 A381824 * A381826 A381827 A381828

Keyword

nonn,easy

Author

Amiram Eldar, Mar 08 2025

Status

approved