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

1,336

Comments

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

Links

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

Formula

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

Example

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.

Prog

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

Crossrefs

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

Cf. also A324539.

Sequence in context: A353370 A355940 A348033 * A133943 A014084 A014159

Adjacent sequences: A327150 A327151 A327152 * A327154 A327155 A327156

Keyword

nonn

Author

Antti Karttunen, Sep 18 2019

Status

approved