A344737 Numbers that are the sum of three fourth powers in eight or more ways.

5745705602, 8185089458, 11054952818, 14355295682, 21789116258, 22247419922, 26839201298, 29428835618, 31861462178, 37314202562, 38214512882, 41923075922, 46543615202, 49511121842, 51711350418, 54438780578, 56255300738, 59223741122, 62862779042, 63429959138

Offset

1,1

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..100

Example

5745705602 is a term because 5745705602 = 3^4 + 230^4 + 233^4 = 25^4 + 218^4 + 243^4 = 43^4 + 207^4 + 250^4 = 58^4 + 197^4 + 255^4 = 85^4 + 177^4 + 262^4 = 90^4 + 173^4 + 263^4 = 102^4 + 163^4 + 265^4 = 122^4 + 145^4 + 267^4.

Prog

(Python)
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1, 1000)]
for pos in cwr(power_terms, 3):
    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. A344729, A344738, A344750, A344924, A345087.

Sequence in context: A322697 A365144 A114260 * A344738 A113644 A234059

Adjacent sequences: A344734 A344735 A344736 * A344738 A344739 A344740

Keyword

nonn

Author

David Consiglio, Jr., May 27 2021

Status

approved