A339672 Number of partitions of n into 7 distinct and relatively prime parts.

1, 1, 2, 3, 5, 7, 11, 15, 21, 28, 38, 49, 65, 82, 105, 131, 164, 201, 248, 300, 364, 436, 522, 618, 733, 860, 1009, 1175, 1366, 1579, 1823, 2093, 2398, 2738, 3117, 3539, 4006, 4526, 5095, 5731, 6419, 7190, 8018, 8946, 9932, 11044, 12213, 13534, 14912, 16475, 18089, 19928, 21808

Offset

28,3

Links

Table of n, a(n) for n=28..80.

Formula

G.f.: Sum_{k>=1} mu(k)* x^(28*k) / Product_{j=1..7} (1 - x^(j*k)).

Mathematica

nmax = 80; CoefficientList[Series[Sum[MoebiusMu[k] x^(28 k)/Product[1 - x^(j k), {j, 1, 7}], {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 28] &

Crossrefs

Cf. A023022, A023027, A023032, A078374, A101271, A340719, A341868, A341870, A341912, A341913, A341914.

Sequence in context: A357660 A309099 A218507 * A026813 A008636 A008630

Adjacent sequences: A339669 A339670 A339671 * A339673 A339674 A339675

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 23 2021

Status

approved