A003996 Sums of distinct nonzero squares in more than one way.

25, 26, 29, 30, 41, 45, 46, 49, 50, 53, 54, 61, 62, 65, 66, 69, 70, 74, 75, 77, 78, 79, 81, 82, 84, 85, 86, 87, 89, 90, 91, 93, 94, 95, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

The largest integer not in this sequence is 132. Proof based on Theorem 3 from M. J. Wiener link: All the numbers from 148+1 to 148+12^2 are the sum of distinct squares from {1^2,...,11^2} in more than one way (direct calculation). This range can be extended indefinitely by adding 12^2, 13^2, etc. Numbers between 132 and 148 confirmed from A033461. - Martin Fuller, Aug 28 2023

Links

• M. J. Wiener, The Largest Integer Not the Sum of Distinct 8th Powers, J. Integer Sequences, 26 (2023), Article 23.5.4.
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A033461, A003995.

Formula

For n >= 65, a(n) = n + 68 (see comment). - Martin Fuller, Aug 28 2023