cp's OEIS Frontend

A113851 Numbers whose prime factors are raised to the sixth power.

%I A113851 #28 Feb 26 2025 01:58:43
%S A113851 64,729,15625,46656,117649,1000000,1771561,4826809,7529536,11390625,
%T A113851 24137569,47045881,85766121,113379904,148035889,308915776,594823321,
%U A113851 729000000,887503681,1291467969,1544804416,1838265625,2565726409,3010936384,3518743761,4750104241
%N A113851 Numbers whose prime factors are raised to the sixth power.
%H A113851 Nathaniel Johnston, <a href="/A113851/b113851.txt">Table of n, a(n) for n = 1..5000</a>
%F A113851 a(n) = A005117(n+1)^6. - _Nathaniel Johnston_, Jun 21 2011
%F A113851 Sum_{n>=1} 1/a(n) = zeta(6)/zeta(12) - 1 = A269404 - 1. - _Amiram Eldar_, Oct 13 2020
%p A113851 for n from 2 to 100 do if(numtheory[issqrfree](n))then printf("%d, ", n^6): fi: od: # _Nathaniel Johnston_, Jun 21 2011
%t A113851 Select[ Range@37^6, Union[Last /@ FactorInteger@# ] == {6} &] (* _Robert G. Wilson v_ *)
%t A113851 Select[Range[2, 37], SquareFreeQ]^6 (* _Amiram Eldar_, Oct 13 2020 *)
%o A113851 (Python)
%o A113851 from math import isqrt
%o A113851 from sympy import mobius
%o A113851 def A113851(n):
%o A113851     def f(x): return int(n+1-sum(mobius(k)*(x//k**2) for k in range(2, isqrt(x)+1)))
%o A113851     m, k = n, f(n)
%o A113851     while m != k: m, k = k, f(k)
%o A113851     return m**6 # _Chai Wah Wu_, Feb 25 2025
%Y A113851 Subset of A001014. Superset of A030516.
%Y A113851 Nonunit terms of A329332 column 6 in ascending order.
%Y A113851 Cf. A005117, A269404.
%K A113851 easy,nonn
%O A113851 1,1
%A A113851 _Cino Hilliard_, Jan 25 2006
%E A113851 More terms from _Robert G. Wilson v_, Jan 26 2006