A327166 Number of divisors d of n for which A000005(d)*d is equal to n, where A000005(x) gives the number of divisors of x.

1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1

Offset: 1

Author

Antti Karttunen, Sep 19 2019

Keywords

• nonn

Comments

a(n) tells how many times in total n occurs in A038040.

Examples

			108 has the following twelve divisors: [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108]. Of these, only d=18 and d=27 are such that d*A000005(d) = 108, as 18*6 = 27*4 = 108. Thus a(108) = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000005, A038040.

Cf. also A327153, A327169.

Programs

Mathematica

Table[Sum[If[d*DivisorSigma[0, d] == n, 1, 0], {d, Divisors[n]}], {n, 1, 120}] (* Vaclav Kotesovec, Jul 23 2022 *)

PARI

A327166(n) = sumdiv(n,d,(d*numdiv(d))==n);

Formula

a(n) = Sum_{d|n} [A000005(d)*d == n], where [ ] is the Iverson bracket.