A345481 Numbers that are the sum of seven squares in four or more ways.

37, 40, 42, 45, 46, 48, 49, 50, 52, 53, 54, 55, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108

Offset

1,1

Links

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Example

40 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2 + 4^2
   = 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 5^2
   = 1^2 + 2^2 + 2^2 + 2^2 + 3^2 + 3^2 + 3^2
   = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2
so 40 is a term.

Prog

(Python)
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**2 for x in range(1, 1000)]
for pos in cwr(power_terms, 7):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 4])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A344808, A345480, A345482, A345491, A345522.

Sequence in context: A041683 A064172 A242989 * A295801 A111198 A081645

Adjacent sequences: A345478 A345479 A345480 * A345482 A345483 A345484

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved