cp's OEIS Frontend

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).

%I A381825 #8 Mar 09 2025 12:27:48
%S A381825 1,27,125,243,343,1331,2187,2197,3125,3375,4913,6859,9261,12167,16807,
%T A381825 19683,24389,29791,30375,35937,42875,50653,59319,68921,78125,79507,
%U A381825 83349,84375,103823,132651,148877,161051,166375,177147,185193,205379,226981,273375,274625
%N 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).
%C A381825 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, ... .
%H A381825 Amiram Eldar, <a href="/A381825/b381825.txt">Table of n, a(n) for n = 1..10000</a>
%F A381825 Sum_{n>=1} 1/a(n) = Product_{prime p >= 3} (1 + 1/(p*(p^2-1))) = (6/7) * A065487 = 1.05539241333308876809... .
%t A381825 Join[{1}, Select[Range[3, 300000, 2], AllTrue[FactorInteger[#][[;;, 2]],  #1 > 1 && OddQ[#1] &] &]]
%o A381825 (PARI) isok(k) = k == 1 || (k % 2 && #select(x -> (x == 1) || !(x % 2), factor(k)[, 2]) == 0);
%Y A381825 Intersection of A005408 and A335988.
%Y A381825 Intersection A036966 and A376218.
%Y A381825 Subsequence of A381824.
%Y A381825 A369118 is a subsequence.
%Y A381825 Cf. A065487.
%K A381825 nonn,easy
%O A381825 1,2
%A A381825 _Amiram Eldar_, Mar 08 2025