A344645 Numbers that are the sum of four fifth powers in exactly two ways.

51445, 876733, 1646240, 3558289, 4062500, 5687000, 7962869, 8227494, 9792364, 9924675, 10908544, 12501135, 15249850, 18317994, 18804544, 20611151, 20983875, 21297837, 23944908, 24201342, 24598407, 27806867, 28055456, 29480343, 31584102, 32557875, 32814683, 35469555, 40882844, 45177175

Offset

1,1

Comments

Differs from A344644 at term 508 because 1479604544 = 3^5 + 49^5 + 53^5 + 62^5 = 14^5 + 37^5 + 52^5 + 65^5 = 19^5 + 37^5 + 45^5 + 67^5

Links

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

Example

1646240 is a term because 1646240 = 9^5 + 15^5 + 15^5 + 15^5 = 11^5 + 13^5 + 13^5 + 17^5

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, 4):
    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. A342686, A344193, A344642, A344644.

Sequence in context: A203405 A152512 A344644 * A203354 A289823 A147530

Adjacent sequences: A344642 A344643 A344644 * A344646 A344647 A344648

Keyword

nonn

Author

David Consiglio, Jr., May 25 2021

Status

approved