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 A344643 Numbers that are the sum of five fifth powers in exactly one way. 6
 5, 36, 67, 98, 129, 160, 247, 278, 309, 340, 371, 489, 520, 551, 582, 731, 762, 793, 973, 1004, 1028, 1059, 1090, 1121, 1152, 1215, 1270, 1301, 1332, 1363, 1512, 1543, 1574, 1754, 1785, 1996, 2051, 2082, 2113, 2144, 2293, 2324, 2355, 2535, 2566, 2777, 3074, 3105, 3129, 3136, 3160, 3191, 3222, 3253, 3316, 3347, 3371 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Differs from A003350 at term 67 because 4097 = 1^5 + 4^5 + 4^5 + 4^5 + 4^5 = 3^5 + 3^5 + 3^5 + 3^5 + 6^5 LINKS David Consiglio, Jr., Table of n, a(n) for n = 1..20000 EXAMPLE 67 is a term because 67 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 PROG (Python) from itertools import combinations_with_replacement as cwr from collections import defaultdict keep = defaultdict(lambda: 0) power_terms = [x**5 for x in range(1, 500)] for pos in cwr(power_terms, 5):     tot = sum(pos)     keep[tot] += 1 rets = sorted([k for k, v in keep.items() if v == 1]) for x in range(len(rets)):     print(rets[x]) CROSSREFS Cf. A003350, A342686, A344190, A344642, A346356. Sequence in context: A073456 A275223 A003350 * A217166 A275143 A276249 Adjacent sequences:  A344640 A344641 A344642 * A344644 A344645 A344646 KEYWORD nonn AUTHOR David Consiglio, Jr., May 25 2021 STATUS approved

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Last modified September 24 09:10 EDT 2021. Contains 347630 sequences. (Running on oeis4.)