A341868 Number of partitions of n into 4 distinct and relatively prime parts.

1, 1, 2, 3, 5, 6, 9, 11, 15, 18, 22, 27, 33, 39, 45, 54, 61, 72, 79, 94, 101, 120, 127, 149, 158, 185, 189, 225, 231, 267, 274, 321, 319, 378, 377, 435, 439, 511, 495, 588, 577, 661, 656, 764, 729, 863, 836, 954, 939, 1089, 1022, 1215, 1165, 1323, 1289, 1492, 1392, 1650, 1566, 1776, 1715

Offset

10,3

Links

Table of n, a(n) for n=10..70.

Formula

G.f.: Sum_{k>=1} mu(k)* x^(10*k) / Product_{j=1..4} (1 - x^(j*k)).

Mathematica

nmax = 70; CoefficientList[Series[Sum[MoebiusMu[k] x^(10 k)/Product[1 - x^(j k), {j, 1, 4}], {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 10] &

Crossrefs

Cf. A000742, A023022, A023024, A078374, A101271, A339672, A340719, A341870, A341912, A341913, A341914.

Sequence in context: A341123 A365877 A325863 * A342497 A028309 A242717

Adjacent sequences: A341865 A341866 A341867 * A341869 A341870 A341871

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 23 2021

Status

approved