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

1,108

Comments

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A038040.

Cf. also A327153, A327169.

Sequence in context: A067898 A010106 A096159 * A024155 A251570 A292241

Adjacent sequences: A327163 A327164 A327165 * A327167 A327168 A327169

Keyword

nonn

Author

Antti Karttunen, Sep 19 2019

Status

approved