A342686 - OEIS

A342686

Numbers that are the sum of five fifth powers in exactly two ways.

4097, 51446, 51477, 51688, 52469, 54570, 59221, 68252, 68905, 84213, 110494, 131104, 151445, 212496, 300277, 325174, 325713, 355114, 422135, 422738, 589269, 637418, 794434, 810820, 876734, 876765, 876976, 877757, 879858, 884509, 893540, 909501, 924912, 935782, 976733, 995571, 1037784, 1083457

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

This sequence differs from A342685:

13124675 = 1^5 + 9^5 + 10^5 + 20^5 + 25^5

= 2^5 + 5^5 + 12^5 + 23^5 + 23^5

= 16^5 + 19^5 + 20^5 + 20^5 + 20^5,

so 13124675 is in A342685, but is not in this sequence.

LINKS

David Consiglio, Jr., Table of n, a(n) for n = 1..20000

EXAMPLE

51477 = 2^5 + 4^5 + 7^5 + 7^5 + 7^5

= 2^5 + 5^5 + 6^5 + 6^5 + 8^5

so 51477 is a term of this sequence.

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, 500)]

for pos in cwr(power_terms, 5):

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. A342685, A342688, A344237, A344643, A344645, A346357.

Sequence in context: A044887 A217196 A342685 * A321809 A017687 A013960

Adjacent sequences: A342683 A342684 A342685 * A342687 A342688 A342689

KEYWORD

nonn

AUTHOR

David Consiglio, Jr., May 18 2021

STATUS

approved

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