A345485 Numbers that are the sum of seven squares in eight or more ways.

61, 66, 69, 70, 72, 73, 76, 77, 78, 79, 81, 82, 84, 85, 86, 87, 88, 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, 121, 122, 123, 124, 125, 126, 127, 128, 129

Offset

1,1

Links

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

Example

66 is a term because 66 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 5^2 + 6^2 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 7^2 = 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 5^2 + 5^2 = 1^2 + 1^2 + 1^2 + 3^2 + 3^2 + 3^2 + 6^2 = 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 4^2 + 6^2 = 1^2 + 2^2 + 2^2 + 3^2 + 4^2 + 4^2 + 4^2 = 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 3^2 + 5^2 = 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 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, 7):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 8])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A344812, A345484, A345486, A345495, A345526.

Sequence in context: A195378 A260561 A346808 * A295805 A295157 A095575

Adjacent sequences: A345482 A345483 A345484 * A345486 A345487 A345488

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved