A344928 Numbers that are the sum of four fourth powers in ten or more ways.

592417938, 677125218, 780595299, 781388643, 803898018, 806692194, 937239954, 940415058, 980421939, 1164012003, 1269819378, 1355899923, 1403089314, 1488645939, 1539221154, 1599073938, 1635878754, 1657885698, 1666044963, 1701067683, 1734489603, 1758151458

Offset

1,1

Links

Sean A. Irvine, Table of n, a(n) for n = 1..2061

Example

592417938 is a term because 592417938 = 6^4 + 59^4 + 65^4 + 154^4  = 7^4 + 11^4 + 20^4 + 156^4  = 10^4 + 17^4 + 17^4 + 156^4  = 12^4 + 112^4 + 115^4 + 127^4  = 15^4 + 86^4 + 107^4 + 142^4  = 21^4 + 49^4 + 70^4 + 154^4  = 25^4 + 107^4 + 112^4 + 132^4  = 26^4 + 45^4 + 71^4 + 154^4  = 28^4 + 105^4 + 112^4 + 133^4  = 63^4 + 77^4 + 112^4 + 140^4.

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, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 10])
for x in range(len(rets)):
    print(rets[x])

Crossrefs

Cf. A341897, A344862, A344926, A344929, A345155.

Sequence in context: A297448 A057535 A134858 * A344929 A145277 A253166

Adjacent sequences: A344925 A344926 A344927 * A344929 A344930 A344931

Keyword

nonn

Author

David Consiglio, Jr., Jun 02 2021

Extensions

More terms from Sean A. Irvine, Jun 03 2021

Status

approved