A344929 - OEIS

%I #8 Jul 31 2021 22:12:28

%S 592417938,806692194,940415058,980421939,1269819378,1355899923,

%T 1488645939,1599073938,1635878754,1657885698,1666044963,1758151458,

%U 1797373314,1813434483,1991146899,2064726483,2198975058,2246905683,2266525314,2302589298,2302698258,2502041283

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

%C 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.

%H Sean A. Irvine, <a href="/A344929/b344929.txt">Table of n, a(n) for n = 1..1446</a>

%e 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.

%o (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**4 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 4):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v == 10])

%o for x in range(len(rets)):

%o     print(rets[x])

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

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 02 2021

%E More terms from _Sean A. Irvine_, Jun 03 2021