A281477 Expansion of Sum_{k>=1} x^(prime(k)^2)/(1 + x^(prime(k)^2)) * Product_{k>=1} (1 + x^(prime(k)^2)).
0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1
Keywords
Examples
a(38) = 3 because we have [25, 9, 4].
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
- Ilya Gutkovskiy, Extended graphical example
- Index entries for related partition-counting sequences
Programs
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Maple
Primes:= select(isprime, [$1..20]): g:= add(x^(p^2)/(1+x^(p^2)),p=Primes)*mul(1+x^(p^2),p=Primes): S:= series(g, x, 20^2+1): seq(coeff(S,x,n),n=1..20^2); # Robert Israel, Feb 08 2017
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Mathematica
nmax = 125; Rest[CoefficientList[Series[Sum[x^Prime[k]^2/(1 + x^Prime[k]^2), {k, 1, nmax}] Product[1 + x^Prime[k]^2, {k, 1, nmax}], {x, 0, nmax}], x]]
Formula
G.f.: Sum_{k>=1} x^(prime(k)^2)/(1 + x^(prime(k)^2)) * Product_{k>=1} (1 + x^(prime(k)^2)).
Comments