A345595 Numbers that are the sum of ten fourth powers in two or more ways.

265, 280, 295, 310, 325, 340, 345, 355, 360, 375, 390, 405, 420, 425, 440, 455, 470, 485, 505, 520, 535, 550, 565, 580, 585, 595, 600, 615, 630, 645, 660, 665, 680, 695, 710, 725, 745, 760, 775, 790, 805, 820, 835, 840, 855, 870, 885, 889, 900, 904, 919, 920

Offset

1,1

Links

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Example

280 is a term because 280 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.

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, 10):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 2])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A003344, A345550, A345586, A345596, A345634, A345854.

Sequence in context: A289639 A283665 A151602 * A345854 A051976 A255085

Adjacent sequences: A345592 A345593 A345594 * A345596 A345597 A345598

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved