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 A344190 Numbers that are the sum of five fourth powers in exactly one way. 6
 5, 20, 35, 50, 65, 80, 85, 100, 115, 130, 145, 165, 180, 195, 210, 245, 290, 305, 320, 325, 355, 370, 385, 405, 420, 435, 450, 500, 530, 545, 560, 580, 595, 610, 625, 629, 644, 659, 674, 675, 689, 690, 709, 724, 739, 754, 755, 770, 785, 789, 800, 804, 819, 850, 865, 869, 899, 914, 929, 930, 949, 964, 979, 994, 1025, 1040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Differs from A003339 at term 17 because 260 = 1^4 + 1^4 + 1^4 + 1^4 + 4^4 = 1^4 + 2^4 + 3^4 + 3^4 + 3^4 LINKS David Consiglio, Jr., Table of n, a(n) for n = 1..20000 EXAMPLE 35 is a member of this sequence because 35 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 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, 50)] 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. A003339, A048926, A344189, A344237, A344643, A345813. Sequence in context: A101867 A003339 A047716 * A326005 A063110 A044066 Adjacent sequences:  A344187 A344188 A344189 * A344191 A344192 A344193 KEYWORD nonn,changed AUTHOR David Consiglio, Jr., May 11 2021 STATUS approved

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Last modified August 5 15:16 EDT 2021. Contains 346472 sequences. (Running on oeis4.)