cp's OEIS Frontend

A295931 Number of ways to write n in the form n = (x^y)^z where x, y, and z are positive integers.

%I A295931 #20 Dec 19 2017 16:08:24
%S A295931 1,1,1,3,1,1,1,3,3,1,1,1,1,1,1,6,1,1,1,1,1,1,1,1,3,1,3,1,1,1,1,3,1,1,
%T A295931 1,3,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,9,1,1,1,1,
%U A295931 1,1,1,1,1,1,1,1,1,1,1,1,6,1,1,1,1,1,1
%N A295931 Number of ways to write n in the form n = (x^y)^z where x, y, and z are positive integers.
%C A295931 By convention a(1) = 1.
%C A295931 Values can be 1, 3, 6, 9, 10, 15, 18, 21, 27, 28, 30, 36, 45, 54, 60, 63, 84, 90, etc. - _Robert G. Wilson v_, Dec 10 2017
%H A295931 Robert Israel, <a href="/A295931/b295931.txt">Table of n, a(n) for n = 1..10000</a>
%F A295931 a(A175082(k)) = 1, a(A093771(k)) = 3.
%F A295931 a(n) = Sum_{d|A052409(n)} A000005(d).
%e A295931 The a(256) = 10 ways are:
%e A295931 (2^1)^8    (2^2)^4   (2^4)^2  (2^8)^1
%e A295931 (4^1)^4    (4^2)^2   (4^4)^1
%e A295931 (16^1)^2   (16^2)^1
%e A295931 (256^1)^1
%p A295931 f:= proc(n) local m,d,t;
%p A295931   m:= igcd(seq(t[2],t=ifactors(n)[2]));
%p A295931   add(numtheory:-tau(d),d=numtheory:-divisors(m))
%p A295931 end proc:
%p A295931 f(1):= 1:
%p A295931 map(f, [$1..100]); # _Robert Israel_, Dec 19 2017
%t A295931 Table[Sum[DivisorSigma[0,d],{d,Divisors[GCD@@FactorInteger[n][[All,2]]]}],{n,100}]
%Y A295931 Cf. A000005, A007425, A052409, A052410, A089723, A093771, A175082, A277562, A281113, A284639, A294786, A294336, A294338, A295920, A295923, A295924, A295935.
%K A295931 nonn
%O A295931 1,4
%A A295931 _Gus Wiseman_, Nov 29 2017