A344811 Numbers that are the sum of six squares in seven or more ways.

60, 65, 68, 69, 77, 78, 81, 84, 86, 87, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136

Offset

1,1

Links

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

Example

65 = 1^2 + 1^2 + 1^2 + 1^2 + 5^2 + 6^2
   = 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 7^2
   = 1^2 + 1^2 + 2^2 + 3^2 + 5^2 + 5^2
   = 1^2 + 1^2 + 3^2 + 3^2 + 3^2 + 6^2
   = 1^2 + 2^2 + 2^2 + 2^2 + 4^2 + 6^2
   = 2^2 + 2^2 + 3^2 + 4^2 + 4^2 + 4^2
   = 2^2 + 3^2 + 3^2 + 3^2 + 3^2 + 5^2
so 65 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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 7])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A344800, A344810, A344812, A345484, A345516.

Sequence in context: A181463 A114559 A175102 * A295697 A138690 A118155

Adjacent sequences: A344808 A344809 A344810 * A344812 A344813 A344814

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved