A344809 Numbers that are the sum of six squares in five or more ways.

54, 57, 60, 62, 63, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 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, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120

Offset

1,1

Links

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

Example

57 is a term because 57 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 7^2 = 1^2 + 1^2 + 1^2 + 2^2 + 5^2 + 5^2 = 1^2 + 1^2 + 1^2 + 3^2 + 3^2 + 6^2 = 1^2 + 2^2 + 2^2 + 4^2 + 4^2 + 4^2 = 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 5^2 = 2^2 + 2^2 + 2^2 + 2^2 + 4^2 + 5^2.

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 >= 5])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A344798, A344808, A344810, A345482, A345514.

Sequence in context: A252722 A326181 A300447 * A344810 A295696 A095561

Adjacent sequences: A344806 A344807 A344808 * A344810 A344811 A344812

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved