A345823 Numbers that are the sum of seven fourth powers in exactly one ways.

7, 22, 37, 52, 67, 82, 87, 97, 102, 112, 117, 132, 147, 162, 167, 177, 182, 197, 212, 227, 242, 247, 322, 327, 337, 352, 387, 402, 407, 417, 452, 467, 482, 487, 562, 567, 577, 582, 592, 627, 631, 642, 646, 657, 661, 662, 676, 691, 692, 706, 707, 711, 721, 722

Offset

1,1

Comments

Differs from A003341 at term 23 because 262 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Example

22 is a term because 22 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 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, 1000)]
for pos in cwr(power_terms, 7):
    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. A003341, A345773, A345813, A345824, A345833, A346278.

Sequence in context: A063157 A375210 A003341 * A161447 A047718 A031053

Adjacent sequences: A345820 A345821 A345822 * A345824 A345825 A345826

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved