A344929 Numbers that are the sum of four fourth powers in exactly ten ways.

592417938, 806692194, 940415058, 980421939, 1269819378, 1355899923, 1488645939, 1599073938, 1635878754, 1657885698, 1666044963, 1758151458, 1797373314, 1813434483, 1991146899, 2064726483, 2198975058, 2246905683, 2266525314, 2302589298, 2302698258, 2502041283

Offset

1,1

Comments

Differs from A344928 at term 2 because 677125218 = 2^4 + 109^4 + 111^4 + 140^4 = 21^4 + 98^4 + 119^4 + 140^4 = 27^4 + 94^4 + 121^4 + 140^4 = 28^4 + 35^4 + 42^4 + 161^4 = 34^4 + 89^4 + 123^4 + 140^4 = 36^4 + 98^4 + 109^4 + 145^4 = 44^4 + 75^4 + 128^4 + 139^4 = 49^4 + 77^4 + 126^4 + 140^4 = 61^4 + 66^4 + 127^4 + 140^4 = 70^4 + 119^4 + 119^4 + 126^4 = 75^4 + 76^4 + 98^4 + 151^4.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..1446

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. A341898, A344861, A344927, A344928, A345156.

Sequence in context: A057535 A134858 A344928 * A145277 A253166 A236948

Adjacent sequences: A344926 A344927 A344928 * A344930 A344931 A344932

Keyword

nonn

Author

David Consiglio, Jr., Jun 02 2021

Extensions

More terms from Sean A. Irvine, Jun 03 2021

Status

approved