A299796 Largest number k that is not the sum of 3 squares and a nonnegative (2n+5)-th power.

2160, 19568, 177136, 1594304, 14348784, 129140160, 1162261440, 10460353136, 94143178736, 847288609392, 7625597484912, 68630377364848, 617673396283888, 5559060566555504, 50031545098999664, 450283905890997360, 4052555153018976240, 36472996377170786288

Offset: 1

Author

XU Pingya, Feb 19 2018

Keywords

• nonn

Comments

Subsequence of A004215.

Examples

			2160 is not the sum of 3 squares and a nonnegative 7th power, and all integers larger than 2160 can be represented as the sum of 3 squares and a nonnegative 7th power (see A297970). Thus a(1) = 2160.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A004215, A022552, A297970.

Programs

Mathematica

a[n_]:= Max@Table[4^k (8 Floor[3^(2 n + 5) / 2^(2 k + 3) - 7 / 8] + 7),  {k, 2, n + 1}] Table[a[n], {n, 18}] (* XU Pingya, Nov 30 2018 *)

Formula

a(n) = max_{2<=i<=n+1, j>=0} {4^i*(8j+7) : 4^i*(8j+7) < 3^(2n+5)}.