A341912 - OEIS

A341912

Number of partitions of n into 5 distinct and relatively prime parts.

1, 1, 2, 3, 5, 7, 10, 13, 18, 23, 30, 37, 47, 57, 70, 83, 101, 118, 141, 162, 192, 218, 255, 286, 333, 370, 427, 470, 540, 590, 673, 730, 831, 894, 1014, 1085, 1224, 1305, 1469, 1552, 1747, 1841, 2057, 2163, 2418, 2520, 2818, 2933, 3256, 3388, 3765, 3879, 4319, 4452, 4914, 5068

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OFFSET

15,3

LINKS

Table of n, a(n) for n=15..70.

FORMULA

G.f.: Sum_{k>=1} mu(k)* x^(15*k) / Product_{j=1..5} (1 - x^(j*k)).

a(n) <= A001401(n-15). - R. J. Mathar, Feb 28 2021

MATHEMATICA

nmax = 70; CoefficientList[Series[Sum[MoebiusMu[k] x^(15 k)/Product[1 - x^(j k), {j, 1, 5}], {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 15] &

CROSSREFS