cp's OEIS Frontend

A113852 Numbers whose prime factors are raised to the seventh power.

%I A113852 #25 Mar 12 2025 10:37:06
%S A113852 128,2187,78125,279936,823543,10000000,19487171,62748517,105413504,
%T A113852 170859375,410338673,893871739,1801088541,2494357888,3404825447,
%U A113852 8031810176,17249876309,21870000000,27512614111,42618442977,52523350144,64339296875,94931877133,114415582592
%N A113852 Numbers whose prime factors are raised to the seventh power.
%H A113852 Amiram Eldar, <a href="/A113852/b113852.txt">Table of n, a(n) for n = 1..10000</a>
%F A113852 From _Amiram Eldar_, Oct 13 2020: (Start)
%F A113852 a(n) = A005117(n+1)^7.
%F A113852 Sum_{n>=1} 1/a(n) = zeta(7)/zeta(14) - 1. (End)
%t A113852 Select[Range@34^7, Union[Last /@ FactorInteger@# ] == {7} &] (* _Robert G. Wilson v_, Jan 26 2006 *)
%t A113852 Select[Range[2, 34], SquareFreeQ]^7 (* _Amiram Eldar_, Oct 13 2020 *)
%o A113852 (PARI) allpwrfact(n,p) = /* All prime factors are raised to the power p */ { local(x,j,ln,y,flag); for(x=4,n, y=Vec(factor(x)); ln = length(y[1]); flag=0; for(j=1,ln, if(y[2][j]==p,flag++); ); if(flag==ln,print1(x",")); ) }
%o A113852 (Python)
%o A113852 from math import isqrt
%o A113852 from sympy import mobius
%o A113852 def A113852(n):
%o A113852     def f(x): return int(n+1-sum(mobius(k)*(x//k**2) for k in range(2, isqrt(x)+1)))
%o A113852     m, k = n, f(n)
%o A113852     while m != k: m, k = k, f(k)
%o A113852     return m**7 # _Chai Wah Wu_, Feb 25 2025
%Y A113852 Proper subset of A001015.
%Y A113852 Nonunit terms of A329332 column 7 in ascending order.
%Y A113852 Cf. A005117, A013665, A013672.
%K A113852 easy,nonn
%O A113852 1,1
%A A113852 _Cino Hilliard_, Jan 25 2006
%E A113852 More terms from _Robert G. Wilson v_, Jan 26 2006