A339244 Number of partitions of n into relatively prime parts where every part appears at least 2 times.

0, 1, 1, 1, 1, 2, 2, 4, 4, 7, 7, 11, 11, 19, 18, 27, 28, 43, 42, 61, 63, 92, 92, 127, 130, 187, 188, 252, 263, 355, 364, 483, 503, 665, 683, 883, 925, 1203, 1248, 1575, 1663, 2106, 2202, 2756, 2904, 3628, 3813, 4692, 4965, 6118, 6458, 7851, 8342, 10130, 10717

Offset

1,6

Comments

Moebius transform of A007690.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Index entries for sequences related to partitions

Formula

1 + Sum_{n>=1} a(n) * x^n / (1 - x^n) = Product_{n>=1} (1 + x^(3*n)) / (1 - x^(2*n)).

a(n) = Sum_{d|n} mu(n/d) * A007690(d).

a(n) ~ exp(2*Pi*sqrt(n)/3) / (6*sqrt(2)*n). - Vaclav Kotesovec, Dec 09 2020

Example

a(10) = 7 because we have [4, 4, 1, 1], [3, 3, 2, 2], [3, 3, 1, 1, 1, 1], [2, 2, 2, 2, 1, 1], [2, 2, 2, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

Mathematica

A007690[n_] := SeriesCoefficient[Product[(1 + x^(3 k))/(1 - x^(2 k)), {k, 1, n}], {x, 0, n}]; a[n_] := Sum[MoebiusMu[n/d] A007690[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 55}]

Crossrefs

Cf. A000837, A007690.

Sequence in context: A277133 A323539 A280954 * A197122 A064410 A304178

Adjacent sequences: A339241 A339242 A339243 * A339245 A339246 A339247

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 28 2020

Status

approved