A344190 Numbers that are the sum of five fourth powers in exactly one way.

5, 20, 35, 50, 65, 80, 85, 100, 115, 130, 145, 165, 180, 195, 210, 245, 290, 305, 320, 325, 355, 370, 385, 405, 420, 435, 450, 500, 530, 545, 560, 580, 595, 610, 625, 629, 644, 659, 674, 675, 689, 690, 709, 724, 739, 754, 755, 770, 785, 789, 800, 804, 819, 850, 865, 869, 899, 914, 929, 930, 949, 964, 979, 994, 1025, 1040

Offset

1,1

Comments

Differs from A003339 at term 17 because 260 = 1^4 + 1^4 + 1^4 + 1^4 + 4^4 = 1^4 + 2^4 + 3^4 + 3^4 + 3^4

Links

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

Example

35 is a member of this sequence because 35 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4

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, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 1])
for x in range(len(rets)):
    print(rets[x])

Crossrefs

Cf. A003339, A048926, A344189, A344237, A344643, A345813.

Sequence in context: A101867 A003339 A047716 * A326005 A063110 A044066

Adjacent sequences: A344187 A344188 A344189 * A344191 A344192 A344193

Keyword

nonn

Author

David Consiglio, Jr., May 11 2021

Status

approved