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A024937
a(n) = number of 2's in all partitions of n into distinct primes.
2
0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 4, 3, 5, 4, 4, 5, 5, 6, 6, 5, 7, 7, 7, 8, 8, 9, 8, 9, 11, 11, 10, 12, 12, 13, 14, 14, 16, 15, 16, 17, 19, 20, 20, 20, 22, 24, 23, 26, 27, 27, 28, 30, 33, 34, 34, 36, 37, 40, 41, 43, 46, 46, 47, 50, 55, 56, 56, 58, 63, 64
OFFSET
0,19
LINKS
Sean A. Irvine, Java program (github)
FORMULA
G.f.: x^2*Product_{k>1} (1+x^prime(k)). - Vladeta Jovovic, Jul 20 2003
MAPLE
with(numtheory):
b:= proc(n, i) option remember; local g;
if n=0 then [1, 0]
elif i<1 then [0, 0]
else g:= `if`(ithprime(i)>n, [0$2], b(n-ithprime(i), i-1));
b(n, i-1) +g +[0, `if`(i=1, g[1], 0)]
fi
end:
a:= n-> b(n, pi(n))[2]:
seq(a(n), n=0..80); # Sean A. Irvine, after Alois P. Heinz, Jul 29 2019
MATHEMATICA
max = 100; (* number of terms *)
CoefficientList[x^2*Product[1+x^Prime[k], {k, 2, PrimePi[max]}]+O[x]^max, x] (* Jean-François Alcover, Sep 07 2022, after Vladeta Jovovic *)
CROSSREFS
Cf. A024939.
Sequence in context: A255472 A230198 A024939 * A350823 A143977 A115265
KEYWORD
nonn
EXTENSIONS
More terms from Vladeta Jovovic, Jul 20 2003
a(0)-a(6) prepended by Sean A. Irvine, Jul 29 2019
STATUS
approved