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 A346335 Numbers that are the sum of eight fifth powers in exactly ten ways. 6
 15539667, 22932525, 24393600, 24650406, 24952961, 24953742, 25142513, 26001294, 27988486, 28609075, 29309819, 31794336, 32223105, 32527286, 32610600, 32807777, 32890541, 32998317, 33015125, 33187858, 33361339, 33550572, 33659175, 33782597, 34029369, 34073650 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Differs from A345618 at term 7 because 25054306 = 1^5 + 1^5 + 2^5 + 6^5 + 12^5 + 12^5 + 12^5 + 30^5 = 5^5 + 6^5 + 6^5 + 12^5 + 14^5 + 14^5 + 20^5 + 29^5 = 4^5 + 5^5 + 8^5 + 11^5 + 11^5 + 16^5 + 23^5 + 28^5 = 4^5 + 5^5 + 5^5 + 7^5 + 17^5 + 20^5 + 20^5 + 28^5 = 2^5 + 6^5 + 9^5 + 9^5 + 9^5 + 21^5 + 23^5 + 27^5 = 1^5 + 4^5 + 4^5 + 9^5 + 19^5 + 21^5 + 21^5 + 27^5 = 3^5 + 5^5 + 6^5 + 13^5 + 13^5 + 14^5 + 26^5 + 26^5 = 1^5 + 3^5 + 10^5 + 10^5 + 10^5 + 23^5 + 23^5 + 26^5 = 9^5 + 10^5 + 14^5 + 17^5 + 17^5 + 20^5 + 23^5 + 26^5 = 7^5 + 12^5 + 15^5 + 15^5 + 19^5 + 19^5 + 23^5 + 26^5 = 3^5 + 4^5 + 4^5 + 7^5 + 17^5 + 21^5 + 25^5 + 25^5. LINKS Sean A. Irvine, Table of n, a(n) for n = 1..8261 EXAMPLE 15539667 is a term because 15539667 = 1^5 + 7^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 + 27^5 = 1^5 + 4^5 + 7^5 + 9^5 + 13^5 + 13^5 + 13^5 + 27^5 = 1^5 + 1^5 + 7^5 + 7^5 + 10^5 + 16^5 + 19^5 + 26^5 = 1^5 + 1^5 + 2^5 + 10^5 + 12^5 + 17^5 + 18^5 + 26^5 = 2^5 + 2^5 + 3^5 + 8^5 + 9^5 + 16^5 + 23^5 + 24^5 = 4^5 + 11^5 + 13^5 + 13^5 + 15^5 + 15^5 + 22^5 + 24^5 = 5^5 + 6^5 + 13^5 + 15^5 + 15^5 + 19^5 + 20^5 + 24^5 = 3^5 + 10^5 + 12^5 + 12^5 + 18^5 + 18^5 + 20^5 + 24^5 = 6^5 + 9^5 + 11^5 + 11^5 + 15^5 + 21^5 + 22^5 + 22^5 = 3^5 + 5^5 + 10^5 + 19^5 + 19^5 + 20^5 + 20^5 + 21^5. 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, 8): 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]) CROSSREFS Cf. A345618, A345842, A346259, A346334, A346345. Sequence in context: A186050 A121840 A345618 * A004673 A290385 A058909 Adjacent sequences: A346332 A346333 A346334 * A346336 A346337 A346338 KEYWORD nonn AUTHOR David Consiglio, Jr., Jul 13 2021 STATUS approved

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Last modified December 9 23:06 EST 2023. Contains 367696 sequences. (Running on oeis4.)