A344926 Numbers that are the sum of four fourth powers in nine or more ways.
328118259, 385202034, 395613234, 489597858, 592417938, 625839858, 641398338, 674511618, 677125218, 693239634, 699598578, 722302434, 779889314, 780278643, 780595299, 781388643, 782999714, 791204514, 792005379, 797405714, 797935698, 803898018, 805299699
Offset: 1
Keywords
Examples
328118259 is a term 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.
Links
- David Consiglio, Jr., Table of n, a(n) for n = 1..79
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, 4): tot = sum(pos) keep[tot] += 1 rets = sorted([k for k, v in keep.items() if v >= 9]) for x in range(len(rets)): print(rets[x])