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A219199
Number of partitions of n into 5 distinct primes.
7
1, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 1, 4, 0, 4, 1, 4, 2, 6, 1, 6, 2, 6, 4, 8, 2, 10, 5, 9, 6, 11, 5, 13, 6, 14, 10, 16, 9, 18, 11, 19, 15, 21, 14, 22, 16, 25, 22, 26, 20, 29, 25, 31, 29, 32, 29, 35, 34, 39, 39, 38, 39, 43, 45, 48, 50, 46, 53, 53, 57, 57, 66, 55
OFFSET
28,7
LINKS
FORMULA
G.f.: Sum_{0<i_1<i_2<...<i_5} x^(Sum_{j=1..5} prime(i_j)).
a(n) = [x^n*y^5] Product_{i>=1} (1+x^prime(i)*y).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [1, 0$5], `if`(i<1, [0$6],
zip((x, y)->x+y, b(n, i-1), [0, `if`(ithprime(i)>n, [0$5],
b(n-ithprime(i), i-1)[1..5])[]], 0)))
end:
a:= n-> b(n, numtheory[pi](n))[6]:
seq(a(n), n=28..100);
MATHEMATICA
k = 5; 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, 28, 100}] (* Jean-François Alcover, Jan 30 2014, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A219180.
Sequence in context: A329981 A096030 A025815 * A029225 A341977 A309937
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 14 2012
STATUS
approved