A025371 Numbers that are the sum of 4 nonzero squares in 6 or more ways.

90, 124, 130, 133, 135, 138, 147, 148, 150, 154, 156, 157, 159, 162, 163, 165, 166, 170, 171, 172, 174, 175, 177, 178, 180, 182, 183, 186, 187, 188, 189, 190, 193, 195, 196, 198, 199, 201, 202, 203, 205, 207, 210, 213, 214, 215, 217, 218, 219, 220, 222, 223, 225, 226

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A025334, A025362, A025370, A025372, A344799, A345148.

Programs

Python

limit = 226
from functools import lru_cache
sq = [k**2 for k in range(1, int(limit**.5)+2) if k**2 + 3 <= limit]
sqs = set(sq)
@lru_cache(maxsize=None)
def findsums(n, m):
  if m == 1: return {(n, )} if n in sqs else set()
  return set(tuple(sorted(t+(s,))) for s in sqs for t in findsums(n-s, m-1))
print([n for n in range(4, limit+1) if len(findsums(n, 4)) >= 6]) # Michael S. Branicky, Apr 20 2021

Formula

{n: A025428(n) >= 6}. Union of A025372 and A025362. - R. J. Mathar, Jun 15 2018