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A345856 Numbers that are the sum of ten fourth powers in exactly four ways.

%I A345856 #6 Jul 31 2021 20:00:13
%S A345856 1620,2660,2725,2740,2835,2855,2870,2900,2915,2920,2950,2965,2980,
%T A345856 3000,3015,3030,3045,3095,3160,3220,3240,3255,3285,3335,3350,3415,
%U A345856 3430,3460,3479,3510,3525,3544,3559,3574,3589,3639,3654,3685,3700,3719,3765,3784,3799
%N A345856 Numbers that are the sum of ten fourth powers in exactly four ways.
%C A345856 Differs from A345597 at term 11 because 2935 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 + 7^4  = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 6^4 + 6^4  = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 7^4  = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4  = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 7^4.
%H A345856 Sean A. Irvine, <a href="/A345856/b345856.txt">Table of n, a(n) for n = 1..10000</a>
%e A345856 2660 is a term because 2660 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 6^4 + 6^4 = 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4.
%o A345856 (Python)
%o A345856 from itertools import combinations_with_replacement as cwr
%o A345856 from collections import defaultdict
%o A345856 keep = defaultdict(lambda: 0)
%o A345856 power_terms = [x**4 for x in range(1, 1000)]
%o A345856 for pos in cwr(power_terms, 10):
%o A345856     tot = sum(pos)
%o A345856     keep[tot] += 1
%o A345856     rets = sorted([k for k, v in keep.items() if v == 4])
%o A345856     for x in range(len(rets)):
%o A345856         print(rets[x])
%Y A345856 Cf. A345597, A345806, A345846, A345855, A345857, A346349.
%K A345856 nonn
%O A345856 1,1
%A A345856 _David Consiglio, Jr._, Jun 26 2021