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

Author

David Consiglio, Jr., Jun 02 2021

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A341898, A344861, A344927, A344928, A345156.

Programs

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])

Extensions

More terms from Sean A. Irvine, Jun 03 2021