A341460 -id:A341460 - cp's OEIS frontend

A341469 Number of partitions of n into 10 distinct nonprime parts.

1, 0, 1, 1, 2, 2, 4, 3, 6, 7, 10, 11, 17, 17, 25, 28, 38, 44, 57, 64, 82, 95, 117, 136, 168, 189, 231, 264, 317, 366, 433, 490, 579, 660, 770, 877, 1019, 1146, 1327, 1497, 1720, 1940, 2215, 2481, 2825, 3165, 3583, 4008, 4523, 5033, 5664

Offset: 95

Ilya Gutkovskiy, Feb 12 2021

nonn

Cf. A005171, A018252, A096258, A219204, A302479, A341460, A341461, A341462, A341464, A341465, A341466, A341467, A341468.

b:= proc(n, i, t) option remember; `if`(n=0,
      `if`(t=0, 1, 0), `if`(i b(n$2, 10):
seq(a(n), n=95..145);  # Alois P. Heinz, Feb 12 2021

b[n_, i_, t_] := b[n, i, t] = If[n == 0,
     If[t == 0, 1, 0], If[i < t || t < 1, 0, b[n, i - 1, t] +
     If[PrimeQ[i], 0, b[n - i, Min[n - i, i - 1], t - 1]]]];
a[n_] := b[n, n, 10];
Table[a[n], {n, 95, 145}] (* Jean-François Alcover, Feb 28 2022, after Alois P. Heinz *)

A341504 Number of ways to write n as an ordered sum of 10 nonprime numbers.

Original entry on oeis.org

1, 0, 0, 10, 0, 10, 45, 10, 100, 130, 135, 460, 390, 820, 1435, 1552, 3135, 4090, 5805, 9370, 12040, 17890, 25485, 33940, 48385, 65812, 87925, 121040, 160155, 212350, 283666, 368590, 482750, 628390, 806450, 1039382, 1327060, 1682860, 2134730, 2684320, 3364819

Offset: 10

Ilya Gutkovskiy, Feb 13 2021

nonn

Cf. A005171, A018252, A052284, A076608, A340966, A341460, A341469, A341480, A341481, A341482, A341483, A341484, A341485, A341486.

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(isprime(j), 0, b(n-j, t-1)), j=1..n)))
    end:
a:= n-> b(n, 10):
seq(a(n), n=10..50);  # Alois P. Heinz, Feb 13 2021

nmax = 50; CoefficientList[Series[Sum[Boole[!PrimeQ[k]] x^k, {k, 1, nmax}]^10, {x, 0, nmax}], x] // Drop[#, 10] &

cp's OEIS Frontend

A341469 Number of partitions of n into 10 distinct nonprime parts.

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