A299796 -id:A299796 - cp's OEIS frontend

A322122 Number of positive integers that are not the sum of 3 squares and a nonnegative (2n + 1)-st power.

0, 0, 17, 191, 1816, 16541, 149320, 1344880, 12106148, 108960347, 980654368, 8825914594, 79433288194, 714899721602, 6434097782077, 57906880685893, 521161927629204, 4690457351939133, 42214116174823814, 379927045590000351, 3419343410347321718

Offset: 1

XU Pingya, Nov 27 2018

nonn

Wikipedia, Legendre's three-square theorem

Cf. A004215, A297788, A273915, A297970, A296579, A299796.

a[n_]:=Sum[Floor[3^(2n+1)/2^(2k+3)-7/8]+1, {k,2,n-1}];
Table[a[n], {n,21}]

a(n) = Sum_{k=2..n-1} (floor(3^(2n+1)/2^(2k+3)-7/8) + 1).

A332665 a(n) = largest number k that is not the sum of {2 squares, a nonnegative 5th power, and a nonnegative n-th power}.

Original entry on oeis.org

71, 2543, 146687, 55871, 63703, 353087, 606239, 21073228, 4606428, 19212172, 16301375, 88507864, 228238087, 126691212, 121909855, 366845415, 448525727, 1818767247, 1319413228, 341968924, 673747279, 188739607, 2366756975, 1770393855, 411629407, 1240489516

Offset: 3

XU Pingya, Feb 19 2020

nonn

All terms are conjectural and have only been checked up to 4*10^9.

			a(4) = 2543, since 2543 is the greatest number such that is not the sum of {2 squares, a nonnegative 5th power, and a 4th power} (at least up to 4*10^9).

W. Jagy and I. Kaplansky, Sums of Squares, Cubes and Higher Powers, Experimental Mathematics, vol. 4 (1995) pp. 169-173.

Cf. A022566, A111151, A299796.

cp's OEIS Frontend

A322122 Number of positive integers that are not the sum of 3 squares and a nonnegative (2n + 1)-st power.

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