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

1,4096

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

Formula

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A299406 A287769 A267866 * A318924 A356162 A253414

Adjacent sequences: A175084 A175085 A175086 * A175088 A175089 A175090

Keyword

nonn

Author

Jaroslav Krizek, Jan 24 2010

Extensions

More terms from Antti Karttunen, Nov 21 2017

Status

approved