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 A346350 Numbers that are the sum of ten fifth powers in exactly five ways. 6
 200009, 220350, 235658, 329271, 329810, 330052, 359211, 359453, 359498, 360298, 367314, 368529, 374519, 374847, 375089, 375870, 376620, 376651, 377159, 377643, 380283, 382622, 384395, 384934, 387035, 388933, 391736, 392064, 392275, 392339, 392517, 392581 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Differs from A345637 at term 29 because 392095 = 2^5 + 2^5 + 2^5 + 4^5 + 5^5 + 5^5 + 5^5 + 8^5 + 10^5 + 12^5 = 1^5 + 1^5 + 1^5 + 5^5 + 6^5 + 6^5 + 6^5 + 7^5 + 10^5 + 12^5 = 2^5 + 2^5 + 2^5 + 3^5 + 3^5 + 6^5 + 7^5 + 9^5 + 9^5 + 12^5 = 2^5 + 2^5 + 2^5 + 4^5 + 4^5 + 4^5 + 6^5 + 9^5 + 11^5 + 11^5 = 1^5 + 2^5 + 2^5 + 3^5 + 4^5 + 5^5 + 8^5 + 8^5 + 11^5 + 11^5 = 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 8^5 + 9^5 + 10^5 + 10^5 + 10^5. LINKS Sean A. Irvine, Table of n, a(n) for n = 1..10000 EXAMPLE 200009 is a term because 200009 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 6^5 + 6^5 + 6^5 + 9^5 + 10^5 = 1^5 + 3^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 8^5 + 8^5 + 10^5 = 1^5 + 3^5 + 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 7^5 + 8^5 + 10^5 = 2^5 + 2^5 + 4^5 + 4^5 + 6^5 + 8^5 + 8^5 + 8^5 + 8^5 + 9^5 = 1^5 + 2^5 + 3^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5. 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, 1000)] for pos in cwr(power_terms, 10): tot = sum(pos) keep[tot] += 1 rets = sorted([k for k, v in keep.items() if v == 5]) for x in range(len(rets)): print(rets[x]) CROSSREFS Cf. A345637, A345857, A346340, A346349, A346351. Sequence in context: A094800 A200863 A345637 * A345661 A363167 A179224 Adjacent sequences: A346347 A346348 A346349 * A346351 A346352 A346353 KEYWORD nonn AUTHOR David Consiglio, Jr., Jul 13 2021 STATUS approved

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Last modified December 5 01:00 EST 2023. Contains 367565 sequences. (Running on oeis4.)