A365126 Number of representations of n as the sum of a prime number and a fourth power of a nonnegative integer.

0, 1, 2, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 2, 1, 1, 0, 2, 1, 0, 0, 1, 0, 2, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 2, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 3, 2, 0, 1, 1, 1, 2, 1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 2, 0, 1, 2, 1, 0, 0, 1, 1, 1

Offset

1,3

Links

Table of n, a(n) for n=1..119.

Formula

G.f.: (Sum_{i>=1} x^prime(i)) * (Sum_{j>=0} x^(j^4)).

Mathematica

nmax = 120; CoefficientList[Series[Sum[x^Prime[i], {i, 1, nmax}] Sum[x^j^4, {j, 0, nmax^(1/4)}], {x, 0, nmax}], x] // Rest

Crossrefs

Cf. A002471, A302354, A365127, A365166, A365167.

Sequence in context: A037819 A090405 A237837 * A168509 A347822 A079635

Adjacent sequences: A365123 A365124 A365125 * A365127 A365128 A365129

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 24 2023

Status

approved