A341897 Numbers that are the sum of five fourth powers in ten or more ways.

954979, 1205539, 1574850, 1713859, 1801459, 1863859, 1877394, 1882579, 2071939, 2109730, 2138419, 2142594, 2157874, 2225859, 2288179, 2419954, 2492434, 2495939, 2605314, 2663539, 2711394, 2784499, 2835939, 2847394, 2849859, 2880994, 2919154, 2924674, 3007474

Offset

1,1

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Example

954979 is a term because 954979 = 1^4 + 2^4 + 11^4 + 19^4 + 30^4  = 1^4 + 7^4 + 18^4 + 25^4 + 26^4  = 3^4 + 8^4 + 17^4 + 20^4 + 29^4  = 4^4 + 8^4 + 13^4 + 25^4 + 27^4  = 4^4 + 9^4 + 10^4 + 11^4 + 31^4  = 6^4 + 6^4 + 15^4 + 21^4 + 29^4  = 7^4 + 10^4 + 18^4 + 19^4 + 29^4  = 11^4 + 11^4 + 20^4 + 22^4 + 27^4  = 16^4 + 17^4 + 17^4 + 24^4 + 25^4  = 18^4 + 19^4 + 20^4 + 23^4 + 23^4.

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, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 10])
for x in range(len(rets)):
    print(rets[x])

Crossrefs

Cf. A341891, A341898, A344928, A345187, A345567.

Sequence in context: A203823 A251911 A224593 * A341898 A092377 A348123

Adjacent sequences: A341894 A341895 A341896 * A341898 A341899 A341900

Keyword

nonn

Author

David Consiglio, Jr., Jun 04 2021

Status

approved