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 A345852 Numbers that are the sum of nine fourth powers in exactly ten ways. 7
 9299, 12708, 12948, 13269, 13349, 13524, 13589, 13764, 13829, 13893, 14133, 14228, 14468, 14564, 14869, 14934, 14964, 15014, 15094, 15109, 15174, 15189, 15333, 15428, 15429, 15524, 15588, 15604, 15653, 16214, 16229, 16469, 16564, 16644, 16773, 16883, 16948 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Differs from A345594 at term 15 because 14804 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 8^4 + 8^4 + 9^4 = 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 + 8^4 + 9^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 11^4 = 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 8^4 + 8^4 = 1^4 + 1^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 8^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 6^4 + 9^4 + 9^4 = 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4 + 8^4 + 9^4 = 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 + 8^4 + 9^4 = 2^4 + 4^4 + 4^4 + 4^4 + 4^4 + 7^4 + 7^4 + 7^4 + 9^4 = 2^4 + 6^4 + 6^4 + 6^4 + 6^4 + 7^4 + 7^4 + 7^4 + 7^4 = 3^4 + 4^4 + 4^4 + 4^4 + 6^4 + 6^4 + 7^4 + 7^4 + 9^4. LINKS Sean A. Irvine, Table of n, a(n) for n = 1..10000 EXAMPLE 12708 is a term because 12708 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 10^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 10^4 = 1^4 + 1^4 + 1^4 + 5^4 + 6^4 + 6^4 + 6^4 + 8^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 6^4 + 8^4 + 9^4 = 1^4 + 2^4 + 4^4 + 4^4 + 5^4 + 6^4 + 6^4 + 7^4 + 9^4 = 1^4 + 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 6^4 + 6^4 + 9^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4 + 10^4 = 2^4 + 2^4 + 3^4 + 3^4 + 5^4 + 6^4 + 7^4 + 8^4 + 8^4 = 2^4 + 4^4 + 4^4 + 4^4 + 5^4 + 7^4 + 7^4 + 7^4 + 8^4 = 3^4 + 4^4 + 4^4 + 5^4 + 6^4 + 6^4 + 7^4 + 7^4 + 8^4. PROG (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, 9): 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. A345594, A345802, A345842, A345851, A345862, A346345. Sequence in context: A343193 A237401 A345594 * A257270 A257385 A257266 Adjacent sequences: A345849 A345850 A345851 * A345853 A345854 A345855 KEYWORD nonn AUTHOR David Consiglio, Jr., Jun 26 2021 STATUS approved

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Last modified April 21 00:22 EDT 2024. Contains 371850 sequences. (Running on oeis4.)