A219204 Number of partitions of n into 10 distinct primes.
1, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 3, 0, 1, 0, 4, 0, 5, 0, 3, 0, 7, 0, 9, 0, 7, 1, 10, 0, 16, 0, 9, 1, 18, 1, 25, 1, 16, 2, 30, 2, 35, 1, 25, 4, 45, 3, 53, 2, 45, 8, 62, 4, 79, 6, 67, 14, 90, 8, 112, 10, 96, 19, 126, 16, 158, 17, 135, 29, 182, 26, 210
Offset: 129
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 129..10000
Crossrefs
Column k=10 of A219180.
Programs
-
Maple
b:= proc(n, i) option remember; `if`(n=0, [1,0$10], `if`(i<1, [0$11], zip((x, y)->x+y, b(n, i-1), [0, `if`(ithprime(i)>n, [0$10], b(n-ithprime(i), i-1)[1..10])[]], 0))) end: a:= n-> b(n, numtheory[pi](n))[11]: seq(a(n), n=129..210); -
Mathematica
k = 10; b[n_, i_] := b[n, i] = If[n == 0, Join[{1}, Array[0&, k]], If[i<1, Array[0&, k+1] , Plus @@ PadRight[{b[n, i-1], Join[{0}, If[Prime[i]>n, Array[0&, k], Take[b[n-Prime[i], i-1], k]]]}]]]; a[n_] := b[n, PrimePi[n]][[k+1]]; Table[a[n], {n, 129, 210}] (* Jean-François Alcover, Jan 30 2014, after Alois P. Heinz *) Table[Length@Select[IntegerPartitions[k,{10}, Prime@Range@100], #[[1]] > #[[2]] > #[[3]] > #[[4]] > #[[5]] > #[[6]] > #[[7]] > #[[8]] > #[[9]] > #[[10]] &], {k, 129, 210}] (* Robert Price, Apr 25 2025 *)
Formula
G.f.: Sum_{0
a(n) = [x^n*y^10] Product_{i>=1} (1+x^prime(i)*y).