cp's OEIS Frontend

A175087 Number of numbers whose product of perfect divisors is equal to n.

%I A175087 #20 Jan 09 2023 13:02:29
%S A175087 1,1,1,0,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,
%T A175087 1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A175087 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1
%N A175087 Number of numbers whose product of perfect divisors is equal to n.
%C A175087 Perfect divisor of n is divisor d such that d^k = n for some k >= 1. See A175068 (product of perfect divisors of n), A175084 (possible values for product of perfect divisors of n) and A175085 (numbers m such that product of perfect divisors of x = m has no solution). a(n) = 0 or 1 for all n.
%C A175087 That is, this is the characteristic function of A175084. - _Antti Karttunen_, Nov 21 2017
%H A175087 Antti Karttunen, <a href="/A175087/b175087.txt">Table of n, a(n) for n = 1..16384</a>
%H A175087 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%H A175087 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A175087 a(n) = Sum_{k=1..n} [A175068(k)==n]. - _Antti Karttunen_, Nov 21 2017
%t A175087 With[{nn = 105}, ReplacePart[ConstantArray[0, nn], Flatten@ Table[{i -> 1}, {i, TakeWhile[#, # <= nn &] &@ Union@ Table[Apply[Times, Select[Divisors@ n, Or[# == 1, #^IntegerExponent[n, #] == n] &]], {n, nn}]}] ] ] (* _Michael De Vlieger_, Nov 21 2017 *)
%o A175087 (PARI)
%o A175087 A175068(n) = { my(m=1); fordiv(n,d,if((d>1)&&(d^valuation(n,d))==n,m*=d)); (m); };
%o A175087 A175087(n) = sum(i=1,n,A175068(i)==n); \\ _Antti Karttunen_, Nov 21 2017
%Y A175087 Cf. A175068, A175084 (positions of ones), A175085 (of zeros).
%K A175087 nonn
%O A175087 1,4096
%A A175087 _Jaroslav Krizek_, Jan 24 2010
%E A175087 More terms from _Antti Karttunen_, Nov 21 2017