A307647 -id:A307647 - cp's OEIS frontend

A365168 Numbers that are the sum of a prime number and a fourth power of a positive integer.

3, 4, 6, 8, 12, 14, 18, 19, 20, 21, 23, 24, 27, 29, 30, 32, 33, 35, 38, 39, 42, 44, 45, 47, 48, 53, 54, 57, 59, 60, 62, 63, 68, 69, 72, 74, 75, 77, 80, 83, 84, 86, 87, 88, 89, 90, 92, 94, 95, 98, 99, 100, 102, 104, 105, 108, 110, 112, 113, 114, 117, 118, 119, 122, 123, 124, 125

Offset: 1

Ilya Gutkovskiy, Aug 24 2023

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A058654, A307647, A365127, A365167, A365169.

N:= 200: # for terms up to N
P:= select(isprime,{$2..N-1}):
F:= {seq(i^4,i=1..floor(N^(1/4)))}:
sort(convert({seq(seq(s+t,s=P),t=F)},list)); # Robert Israel, Aug 28 2024

nmax = 125; f[x_] := Sum[x^Prime[i], {i, 1, nmax}] Sum[x^j^4, {j, 1, nmax^(1/4)}]; Exponent[#, x] & /@ List @@ Normal[Series[f[x], {x, 0, nmax}]]

A307646 Numbers that are the sum of a prime number and a nonnegative cube.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24, 25, 27, 29, 30, 31, 32, 34, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 79, 80, 81, 83, 84, 86, 87, 88, 89, 90, 91

Offset: 1

Ilya Gutkovskiy, Apr 19 2019

nonn

Cf. A000040, A000578, A014089, A045911, A302354, A307647.

Exponents in expansion of (Sum_{i>=1} x^prime(i)) * (Sum_{j>=0} x^(j^3)).

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A365168 Numbers that are the sum of a prime number and a fourth power of a positive integer.

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A307646 Numbers that are the sum of a prime number and a nonnegative cube.

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