A023025 -id:A023025 - cp's OEIS frontend

A023035 Number of compositions of n into 10 ordered relatively prime parts.

1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48620, 92377, 167960, 293920, 497420, 817135, 1307504, 2042755, 3124550, 4686110, 6906900, 10013002, 14307150, 20155070, 28048790, 38555660, 52451256, 70583095, 94143280, 124355000

Offset: 10

David W. Wilson

nonn

Marius A. Burtea, Table of n, a(n) for n = 10..5000
N. J. A. Sloane, Transforms

Cf. A000741, A000742, A000743, A023031, A023032, A023033, A023034.

Cf. A023023, A023024, A023025, A023026, A023027, A023028, A023029, A023030.

[&+[MoebiusMu(n div d)*Binomial(d-1, 9):d in Divisors(n)]:n in[10..42]]; // Marius A. Burtea, Feb 07 2020

with(numtheory):
a:= n-> add(mobius(n/d)*binomial(d-1, 9), d=divisors(n)):
seq(a(n), n=10..50);  # Alois P. Heinz, Feb 05 2020

a[n_]:=Sum[Boole[Divisible[n, k]] MoebiusMu[n/k] Binomial[k -1, 9], {k, 1, n}]; Table[a[n], {n, 10, 45}] (* or *) Table[a[n],{n, 9, 45}] a[n_]:=DivisorSum[n, Binomial[#-1,9] MoebiusMu[n/#]&]; Array[a, 37, 10] (* Vincenzo Librandi, Feb 08 2020 *)

Moebius transform of C(n-1,9).

G.f.: Sum_{k>=1} mu(k) * x^(10*k) / (1 - x^k)^10. - Ilya Gutkovskiy, Feb 05 2020

A341912 Number of partitions of n into 5 distinct and relatively prime parts.

Original entry on oeis.org

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

Ilya Gutkovskiy, Feb 23 2021

nonn

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

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] &

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

cp's OEIS Frontend

A023035 Number of compositions of n into 10 ordered relatively prime parts.

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