A341898 - OEIS

%I #15 May 10 2024 02:26:44

%S 954979,1205539,1574850,1713859,1863859,1877394,1882579,2071939,

%T 2109730,2225859,2288179,2419954,2492434,2495939,2605314,2711394,

%U 2784499,2835939,2847394,2880994,2924674,3007474,3061939,3071379,3074179,3117235,3127219,3174834,3190899

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

%C Differs at term 5 because

%C 1801459 =  1^4 +  4^4 +  5^4 + 28^4 + 33^4

%C         =  1^4 +  4^4 + 12^4 + 23^4 + 35^4

%C         =  1^4 +  7^4 + 16^4 + 30^4 + 31^4

%C         =  1^4 + 16^4 + 18^4 + 19^4 + 35^4

%C         =  3^4 +  6^4 + 18^4 + 21^4 + 35^4

%C         =  5^4 +  7^4 + 19^4 + 24^4 + 34^4

%C         =  5^4 +  9^4 + 14^4 + 29^4 + 32^4

%C         =  7^4 +  9^4 + 16^4 + 25^4 + 34^4

%C         =  7^4 + 14^4 + 16^4 + 21^4 + 35^4

%C         =  8^4 +  9^4 + 20^4 + 29^4 + 31^4

%C         = 10^4 + 19^4 + 19^4 + 21^4 + 34^4.

%H David Consiglio, Jr., <a href="/A341898/b341898.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

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

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

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

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

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

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

%e        = 18^4 + 19^4 + 20^4 + 23^4 + 23^4

%e so 954979 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 == 10])

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

%o     print(rets[x])

%Y Cf. A341892, A341897, A344929, A345188, A345822.

%K nonn

%O 1,1

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