A341897 Numbers that are the sum of five fourth powers in ten or more ways.
954979, 1205539, 1574850, 1713859, 1801459, 1863859, 1877394, 1882579, 2071939, 2109730, 2138419, 2142594, 2157874, 2225859, 2288179, 2419954, 2492434, 2495939, 2605314, 2663539, 2711394, 2784499, 2835939, 2847394, 2849859, 2880994, 2919154, 2924674, 3007474
Offset: 1
Keywords
Examples
954979 = 1^4 + 2^4 + 11^4 + 19^4 + 30^4
= 1^4 + 7^4 + 18^4 + 25^4 + 26^4
= 3^4 + 8^4 + 17^4 + 20^4 + 29^4
= 4^4 + 8^4 + 13^4 + 25^4 + 27^4
= 4^4 + 9^4 + 10^4 + 11^4 + 31^4
= 6^4 + 6^4 + 15^4 + 21^4 + 29^4
= 7^4 + 10^4 + 18^4 + 19^4 + 29^4
= 11^4 + 11^4 + 20^4 + 22^4 + 27^4
= 16^4 + 17^4 + 17^4 + 24^4 + 25^4
= 18^4 + 19^4 + 20^4 + 23^4 + 23^4
so 954979 is a term.
Links
- David Consiglio, Jr., Table of n, a(n) for n = 1..10000
Programs
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Python
from itertools import combinations_with_replacement as cwr from collections import defaultdict keep = defaultdict(lambda: 0) power_terms = [x**4 for x in range(1, 1000)] for pos in cwr(power_terms, 5): tot = sum(pos) keep[tot] += 1 rets = sorted([k for k, v in keep.items() if v >= 10]) for x in range(len(rets)): print(rets[x])