A349542 Number of partitions of n into distinct unitary divisors of n.

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2

Offset

0,7

Links

Antti Karttunen, Table of n, a(n) for n = 0..20000

Formula

a(n) = [x^n] Product_{d|n, gcd(d,n/d) = 1} (1 + x^d).

Mathematica

a[n_] := SeriesCoefficient[Product[(1 + Boole[GCD[n/d, d] == 1] x^d), {d, Divisors[n]}], {x, 0, n}]; Table[a[n], {n, 0, 114}]

Prog

(PARI) A349542(n) = if(!n, 1, my(p=1); fordiv(n, d, if(1==gcd(d, n/d), p *= (1 + 'x^d))); polcoeff(p, n)); \\ Antti Karttunen, Nov 22 2021

Crossrefs

Cf. A033630, A066874, A077610, A286851, A293188.

Sequence in context: A307608 A323022 A284562 * A087102 A194309 A369936

Adjacent sequences: A349539 A349540 A349541 * A349543 A349544 A349545

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 21 2021

Status

approved