A341892 - OEIS

%I #14 May 10 2024 02:27:25

%S 619090,775714,1100579,1179379,1186834,1243699,1357315,1367539,

%T 1373859,1422595,1431234,1436419,1511299,1536019,1699234,1734899,

%U 1839874,1858594,1880850,1950355,1951650,1978915,2044819,2052899,2069955,2085139,2101779,2119459,2133234

%N Numbers that are the sum of five fourth powers in exactly nine ways.

%C Differs from A341781 at term 3 because

%C 954979 =  1^4 +  2^4 + 11^4 + 19^4 + 30^4

%C        =  1^4 +  7^4 + 18^4 + 25^4 + 26^4

%C        =  3^4 +  8^4 + 17^4 + 20^4 + 29^4

%C        =  4^4 +  8^4 + 13^4 + 25^4 + 27^4

%C        =  4^4 +  9^4 + 10^4 + 11^4 + 31^4

%C        =  6^4 +  6^4 + 15^4 + 21^4 + 29^4

%C        =  7^4 + 10^4 + 18^4 + 19^4 + 29^4

%C        = 11^4 + 11^4 + 20^4 + 22^4 + 27^4

%C        = 16^4 + 17^4 + 17^4 + 24^4 + 25^4

%C        = 18^4 + 19^4 + 20^4 + 23^4 + 23^4.

%H David Consiglio, Jr., <a href="/A341892/b341892.txt">Table of n, a(n) for n = 1..10000</a>

%e 619090 =  1^4 +  2^4 + 18^4 + 22^4 + 23^4

%e        =  1^4 +  3^4 +  4^4 +  8^4 + 28^4

%e        =  1^4 + 11^4 + 14^4 + 22^4 + 24^4

%e        =  2^4 +  2^4 +  8^4 + 17^4 + 27^4

%e        =  2^4 + 13^4 + 13^4 + 18^4 + 26^4

%e        =  3^4 +  6^4 + 12^4 + 16^4 + 27^4

%e        =  4^4 + 12^4 + 14^4 + 23^4 + 23^4

%e        =  9^4 + 12^4 + 16^4 + 21^4 + 24^4

%e        = 14^4 + 16^4 + 18^4 + 19^4 + 23^4

%e so 619090 is a term.

%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, 5):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v == 9])

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

%o     print(rets[x])

%Y Cf. A341891, A341898, A344927, A344945, A345186, A345821.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 04 2021