A344925 - OEIS

%I #6 Jul 31 2021 22:12:21

%S 13155858,26421474,35965458,39803778,98926434,128198994,143776179,

%T 156279618,210493728,237073554,248075538,255831858,257931378,

%U 269965938,270289698,292967619,293579874,295880274,300120003,301080243,302115843,305670834,309742434,331957458

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

%C Differs from A344924 at term 24 because 328118259 = 2^4 + 77^4 + 109^4 + 111^4  = 8^4 + 79^4 + 93^4 + 121^4  = 18^4 + 79^4 + 97^4 + 119^4  = 21^4 + 77^4 + 98^4 + 119^4  = 27^4 + 77^4 + 94^4 + 121^4  = 34^4 + 77^4 + 89^4 + 123^4  = 46^4 + 57^4 + 103^4 + 119^4  = 49^4 + 77^4 + 77^4 + 126^4  = 61^4 + 66^4 + 77^4 + 127^4.

%H David Consiglio, Jr., <a href="/A344925/b344925.txt">Table of n, a(n) for n = 1..100</a>

%e 13155858 is a term because 13155858 = 1^4 + 16^4 + 19^4 + 60^4  = 3^4 + 6^4 + 21^4 + 60^4  = 10^4 + 18^4 + 31^4 + 59^4  = 12^4 + 27^4 + 45^4 + 54^4  = 15^4 + 44^4 + 46^4 + 47^4  = 18^4 + 25^4 + 41^4 + 56^4  = 29^4 + 30^4 + 44^4 + 53^4  = 35^4 + 36^4 + 38^4 + 53^4.

%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 == 8])

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

%o     print(rets[x])

%Y Cf. A344738, A344923, A344924, A344927, A344945, A345153.

%K nonn

%O 1,1

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