A327153 Number of divisors d of n such that sigma(d)*d is equal to n.

1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1

Offset: 1

Author

Antti Karttunen, Sep 18 2019

Keywords

• nonn

Comments

a(n) tells how many times in total n occurs in A064987.

Examples

			336 has 20 divisors: [1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336]. Only two of them, d=12 and d=14, satisfy sigma(d) = (336/d), thus a(336) = 2.
		

Links

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

Crossrefs

Cf. A000203, A064987, A327165 (positions of nonzero terms).

Cf. also A324539.

Programs

PARI

A327153(n) = sumdiv(n, d, (n==d*sigma(d)));

Formula

a(n) = Sum_{d|n} [A000203(d)*d == n], where [ ] is the Iverson bracket.