A341972 Number of partitions of n into 10 primes (counting 1 as a prime).

1, 1, 2, 2, 4, 4, 7, 7, 11, 11, 17, 16, 24, 23, 32, 30, 43, 39, 56, 51, 71, 63, 89, 78, 111, 97, 134, 116, 164, 139, 197, 166, 232, 194, 275, 227, 324, 265, 374, 305, 438, 351, 505, 403, 578, 460, 665, 522, 760, 592, 859, 668, 978, 751, 1105, 844, 1239, 942, 1394

Offset

10,3

Links

Table of n, a(n) for n=10..68.

Maple

b:= proc(n, i) option remember; series(`if`(n=0, 1,
     `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i)))(
     `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 11)
    end:
a:= n-> coeff(b(n, numtheory[pi](n)), x, 10):
seq(a(n), n=10..68);  # Alois P. Heinz, Feb 24 2021

Mathematica

b[n_, i_] := b[n, i] = Series[If[n == 0, 1,
     If[i < 0, 0, Function[p, If[p > n, 0, x*b[n - p, i]]][
     If[i == 0, 1, Prime[i]]] + b[n, i - 1]]], {x, 0, 11}];
a[n_] := Coefficient[b[n, PrimePi[n]], x, 10];
Table[a[n], {n, 10, 68}] (* Jean-François Alcover, Feb 26 2022, after Alois P. Heinz *)

Crossrefs

Cf. A008578, A034891, A259201, A341719, A341945, A341946, A341947, A341948, A341949, A341950, A341951.

Sequence in context: A341719 A099770 A099383 * A277133 A323539 A280954

Adjacent sequences: A341969 A341970 A341971 * A341973 A341974 A341975

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 24 2021

Status

approved