A340719 Number of partitions of n into 8 distinct and relatively prime parts.

1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 52, 70, 89, 116, 146, 186, 230, 288, 352, 434, 525, 638, 764, 919, 1090, 1297, 1527, 1801, 2104, 2462, 2857, 3319, 3828, 4417, 5066, 5811, 6630, 7563, 8588, 9747, 11018, 12447, 14012, 15760, 17674, 19798, 22122, 24688, 27493, 30573, 33940, 37616

Offset: 36

Author

Ilya Gutkovskiy, Feb 23 2021

Keywords

• nonn

Crossrefs

Cf. A023022, A023028, A023033, A078374, A101271, A339672, A341868, A341870, A341912, A341913, A341914.

Programs

Mathematica

nmax = 88; CoefficientList[Series[Sum[MoebiusMu[k] x^(36 k)/Product[1 - x^(j k), {j, 1, 8}], {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 36] &

Formula

G.f.: Sum_{k>=1} mu(k)* x^(36*k) / Product_{j=1..8} (1 - x^(j*k)).