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

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

Cf. A000743, A023022, A023025, A078374, A101271, A339672, A340719, A341868, A341870, A341913, A341914.

Sequence in context: A008766 A103232 A062684 * A033485 A026811 A001401

Adjacent sequences: A341909 A341910 A341911 * A341913 A341914 A341915

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 23 2021

Status

approved