A282064 Expansion of (x + Sum_{p prime, k>=1} x^(p^k))^3.

0, 0, 0, 1, 3, 6, 10, 15, 18, 22, 27, 33, 37, 45, 48, 52, 54, 60, 60, 69, 69, 79, 81, 87, 79, 93, 87, 97, 99, 114, 99, 120, 111, 130, 126, 150, 135, 168, 141, 160, 147, 177, 144, 189, 156, 183, 162, 201, 157, 213, 171, 214, 189, 231, 168, 237, 189, 244, 201, 261, 177, 270, 201, 261, 210, 282, 192, 297, 216, 283, 228

Offset

0,5

Comments

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

Links

Table of n, a(n) for n=0..70.

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))^3.

Example

a(6) = 10 because we have  [4, 1, 1], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 2, 2], [2, 1, 3], [1, 4, 1], [1, 3, 2], [1, 2, 3] and [1, 1, 4].

Mathematica

nmax = 70; CoefficientList[Series[(x + Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}])^3, {x, 0, nmax}], x]

Crossrefs

Cf. A000961, A098238, A280243, A282062.

Sequence in context: A334130 A054731 A334129 * A029716 A284521 A360029

Adjacent sequences: A282061 A282062 A282063 * A282065 A282066 A282067

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2017

Status

approved