A344242 Numbers that are the sum of four fourth powers in exactly three ways.

16578, 43234, 49329, 53218, 54978, 57154, 93393, 106354, 107649, 108754, 138258, 151219, 160434, 168963, 173539, 177699, 178738, 181138, 183603, 185298, 195378, 195859, 196418, 197154, 197778, 201683, 202419, 209763, 211249, 216594, 217138, 223074, 234274, 235554, 235569, 237249, 237699, 240834

Offset

1,1

Comments

Differs from A344241 at term 36 because 236674 = 1^4 + 2^4 + 7^4 + 22^4 = 3^4 + 6^4 + 18^4 + 19^4 = 7^4 + 14^4 + 16^4 + 19^4 = 8^4 + 16^4 + 17^4 + 17^4

Links

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

Example

49329 is a member of this sequence because 49329 = 2^4 + 2^4 + 12^4 + 13^4 = 4^4 + 8^4 + 9^4 + 14^4 = 6^4 + 9^4 + 12^4 + 12^4

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, 50)]
for pos in cwr(power_terms, 4):
    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. A025405, A344193, A344240, A344241, A344244, A344353.

Sequence in context: A234894 A283028 A344241 * A234374 A234380 A234381

Adjacent sequences: A344239 A344240 A344241 * A344243 A344244 A344245

Keyword

nonn

Author

David Consiglio, Jr., May 12 2021

Status

approved