A342688 Numbers that are the sum of five fifth powers in exactly three ways.

13124675, 28055699, 50043937, 52679923, 53069024, 55097976, 57936559, 60484744, 62260463, 62445305, 70211956, 73133026, 79401728, 80368962, 84766210, 88512249, 93288865, 98824300, 106993391, 113055482, 117173891, 120968132, 123383875, 126416258, 131106051, 131529588, 132022925

Offset

1,1

Comments

Differs from A342687 at term 73 because 287618651 = 9^5 + 22^5 + 28^5 + 28^5 + 49^5 = 10^5 + 14^5 + 27^5 + 38^5 + 47^5 = 12^5 + 13^5 + 24^5 + 42^5 + 45^5 = 12^5 + 21^5 + 23^5 + 31^5 + 49^5.

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Example

50043937 is a term of this sequence because 50043937 = 7^5 + 17^5 + 19^5 + 25^5 + 34^5 = 8^5 + 14^5 + 22^5 + 24^5 + 34^5 = 12^5 + 14^5 + 14^5 + 30^5 + 32^5.

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, 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 == 3])
for x in range(len(rets)):
    print(rets[x])

Crossrefs

Cf. A342686, A342687, A344244, A344519, A346358.

Sequence in context: A283274 A343083 A342687 * A206061 A274026 A344924

Adjacent sequences: A342685 A342686 A342687 * A342689 A342690 A342691

Keyword

nonn

Author

David Consiglio, Jr., May 18 2021

Status

approved