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A175087 Number of numbers whose product of perfect divisors is equal to n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 A253414 A127872

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

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Last modified November 15 11:14 EST 2019. Contains 329144 sequences. (Running on oeis4.)