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A344945 Numbers that are the sum of five fourth powers in exactly eight ways. 7
534130, 654754, 663155, 729219, 737459, 742770, 758354, 810034, 813459, 816579, 831250, 906034, 930499, 954930, 1009954, 1055619, 1083955, 1099459, 1101859, 1103554, 1106019, 1157634, 1167794, 1180003, 1215394, 1217539, 1246354, 1253074, 1255539, 1278690 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Differs from A344944 at term 2 because 619090 = 1^4 + 2^4 + 18^4 + 22^4 + 23^4  = 1^4 + 3^4 + 4^4 + 8^4 + 28^4  = 1^4 + 11^4 + 14^4 + 22^4 + 24^4  = 2^4 + 2^4 + 8^4 + 17^4 + 27^4  = 2^4 + 13^4 + 13^4 + 18^4 + 26^4  = 3^4 + 6^4 + 12^4 + 16^4 + 27^4  = 4^4 + 12^4 + 14^4 + 23^4 + 23^4  = 9^4 + 12^4 + 16^4 + 21^4 + 24^4  = 14^4 + 16^4 + 18^4 + 19^4 + 23^4.

LINKS

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

EXAMPLE

534130 is a term because 534130 = 1^4 + 3^4 + 16^4 + 22^4 + 22^4  = 2^4 + 2^4 + 4^4 + 7^4 + 27^4  = 2^4 + 3^4 + 6^4 + 6^4 + 27^4  = 2^4 + 6^4 + 9^4 + 21^4 + 24^4  = 4^4 + 16^4 + 17^4 + 18^4 + 23^4  = 6^4 + 8^4 + 11^4 + 22^4 + 23^4  = 7^4 + 8^4 + 16^4 + 19^4 + 24^4  = 13^4 + 14^4 + 14^4 + 21^4 + 22^4.

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 == 8])

for x in range(len(rets)):

    print(rets[x])

CROSSREFS

Cf. A341892, A344925, A344943, A344944, A345184, A345820.

Sequence in context: A061730 A235076 A344944 * A269322 A227497 A183650

Adjacent sequences:  A344942 A344943 A344944 * A344946 A344947 A344948

KEYWORD

nonn

AUTHOR

David Consiglio, Jr., Jun 03 2021

STATUS

approved

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Last modified October 22 10:16 EDT 2021. Contains 348160 sequences. (Running on oeis4.)