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

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, 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, 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

Offset: 1

Author

Jaroslav Krizek, Jan 24 2010

Keywords

• nonn

Comments

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.

That is, this is the characteristic function of A175084. - Antti Karttunen, Nov 21 2017

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for characteristic functions
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A175068, A175084 (positions of ones), A175085 (of zeros).

Programs

Mathematica

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 *)

PARI

A175068(n) = { my(m=1); fordiv(n,d,if((d>1)&&(d^valuation(n,d))==n,m*=d)); (m); };
A175087(n) = sum(i=1,n,A175068(i)==n); \\ Antti Karttunen, Nov 21 2017

Formula

a(n) = Sum_{k=1..n} [A175068(k)==n]. - Antti Karttunen, Nov 21 2017

Extensions

More terms from Antti Karttunen, Nov 21 2017