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A132381
Number of partitions of n with exactly one prime number.
2
0, 1, 2, 3, 4, 7, 9, 12, 15, 22, 28, 38, 46, 62, 77, 98, 117, 152, 183, 230, 275, 344, 408, 504, 592, 726, 856, 1038, 1212, 1469, 1712, 2048, 2380, 2839, 3288, 3901, 4500, 5313, 6127, 7193, 8254, 9671, 11081, 12909, 14764, 17153, 19566, 22658, 25786, 29762
OFFSET
1,3
LINKS
EXAMPLE
a(10) = #{8+2, 7+1+1+1, 6+3+1, 6+2+2, 6+2+1+1, 5+5, 5+4+1, 5+1+1+1+1+1, 4+4+2, 4+3+3, 4+3+1+1+1, 4+2+2+2, 4+2+2+1+1, 4+2+1+1+1+1, 3+3+3+1, 3+3+1+1+1+1, 3+1+1+1+1+1+1+1, 2+2+2+2+2, 2+2+2+2+1+1, 2+2+2+1+1+1+1, 2+2+1+1+1+1+1+1, 2+1+1+1+1+1+1+1+1} = 22.
MAPLE
b:= proc(n, i) option remember; local j; if n=0 then [1, 0] elif i<1
then [0$2] else b(n, i-1); for j to n/i do zip((x, y)->x+y, %,
[`if`(isprime(i), 0, NULL), b(n-i*j, i-1)[]], 0) od; %[1..2] fi
end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..60); # Alois P. Heinz, May 29 2013
MATHEMATICA
zip = With[{m = Max[Length[#1], Length[#2]]}, PadRight[#1, m] + PadRight[#2, m]]&; b[n_, i_] := b[n, i] = Module[{j, pc}, Which[n == 0, {1, 0}, i<1, {0, 0}, True, pc = b[n, i-1]; For[j = 1, j <= n/i, j++, pc = zip[pc, Join[{If[PrimeQ[i], 0, Nothing]}, b[n-i*j, i-1]]] ]; pc[[1 ;; 2]] ]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Feb 12 2017, after Alois P. Heinz *)
CROSSREFS
Cf. A002095.
Column k=1 of A274517.
Sequence in context: A084913 A270839 A117450 * A073152 A325092 A375601
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 10 2007
STATUS
approved