A282062 Expansion of (x + Sum_{p prime, k>=1} x^(p^k))^2.

0, 0, 1, 2, 3, 4, 5, 4, 5, 6, 7, 6, 8, 6, 7, 6, 7, 6, 9, 6, 10, 8, 7, 4, 10, 6, 9, 8, 10, 6, 12, 6, 13, 10, 13, 8, 14, 4, 11, 8, 12, 6, 12, 6, 12, 10, 11, 4, 16, 6, 15, 8, 12, 4, 17, 6, 14, 8, 11, 4, 16, 6, 13, 8, 13, 6, 18, 4, 16, 10, 14, 4, 20, 6, 15, 12, 14, 6, 18, 4, 18, 8, 13, 8, 22, 6, 17, 8, 14, 6, 24, 8, 16, 6, 13, 4

Offset

0,4

Comments

Number of ways to write n as an ordered sum of two prime powers (1 included).

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Ilya Gutkovskiy, Extended graphical example

Eric Weisstein's World of Mathematics, Prime Power

Formula

G.f.: (x + Sum_{p prime, k>=1} x^(p^k))^2.

Example

a(8) = 5 because we have  [7, 1], [5, 3], [4, 4], [3, 5] and [1, 7].

Maple

N:= 100: # to get a(0)..a(N)
P:= select(isprime, [$2..N]):
g:= x + add(add(x^(p^k), k=1..floor(log[p](N))), p=P):
S:= series(g^2, x, N+1):
seq(coeff(S, x, n), n=0..N); # Robert Israel, Feb 10 2017

Mathematica

nmax = 95; CoefficientList[Series[(x + Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}])^2, {x, 0, nmax}], x]

Crossrefs

Cf. A000961, A071330, A071331, A073610, A095840, A280242, A282064.

Sequence in context: A205785 A303235 A350774 * A318126 A326167 A308590

Adjacent sequences: A282059 A282060 A282061 * A282063 A282064 A282065

Keyword

nonn,look

Author

Ilya Gutkovskiy, Feb 05 2017

Status

approved