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A346362 Numbers that are the sum of six fifth powers in exactly seven ways. 6
1184966816, 1700336000, 1717860100, 1972000800, 2229475325, 2396275200, 2548597632, 2625460992, 2886251808, 3217068800, 3697267200, 3729261536, 3765398725, 4046532448, 4165116967, 4246566632, 4286704224, 4489548050, 4539955200, 4623694108, 4710031469 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Differs from A345721 at term 6 because 2295937600 = 4^5 + 21^5 + 38^5 + 42^5 + 43^5 + 72^5 = 8^5 + 16^5 + 30^5 + 42^5 + 54^5 + 70^5 = 8^5 + 13^5 + 36^5 + 37^5 + 57^5 + 69^5 = 14^5 + 16^5 + 16^5 + 52^5 + 54^5 + 68^5 = 3^5 + 14^5 + 32^5 + 44^5 + 61^5 + 66^5 = 4^5 + 18^5 + 22^5 + 52^5 + 58^5 + 66^5 = 10^5 + 14^5 + 26^5 + 42^5 + 63^5 + 65^5 = 1^5 + 7^5 + 34^5 + 57^5 + 58^5 + 63^5.

LINKS

Sean A. Irvine, Table of n, a(n) for n = 1..2648

EXAMPLE

1184966816 is a term because 1184966816 = 15^5 + 24^5 + 27^5 + 38^5 + 39^5 + 63^5 = 2^5 + 28^5 + 36^5 + 36^5 + 42^5 + 62^5 = 4^5 + 24^5 + 38^5 + 38^5 + 40^5 + 62^5 = 21^5 + 32^5 + 37^5 + 41^5 + 45^5 + 60^5 = 8^5 + 14^5 + 34^5 + 40^5 + 52^5 + 58^5 = 11^5 + 17^5 + 22^5 + 49^5 + 51^5 + 56^5 = 11^5 + 16^5 + 22^5 + 52^5 + 52^5 + 53^5.

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, 6):

    tot = sum(pos)

    keep[tot] += 1

    rets = sorted([k for k, v in keep.items() if v == 7])

    for x in range(len(rets)):

        print(rets[x])

CROSSREFS

Cf. A345721, A345819, A346284, A346361, A346363.

Sequence in context: A166735 A104933 A345721 * A119333 A309227 A195988

Adjacent sequences:  A346359 A346360 A346361 * A346363 A346364 A346365

KEYWORD

nonn

AUTHOR

David Consiglio, Jr., Jul 13 2021

STATUS

approved

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Last modified December 7 09:15 EST 2021. Contains 349574 sequences. (Running on oeis4.)