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A341892 Numbers that are the sum of five fourth powers in exactly nine ways. 7
619090, 775714, 1100579, 1179379, 1186834, 1243699, 1357315, 1367539, 1373859, 1422595, 1431234, 1436419, 1511299, 1536019, 1699234, 1734899, 1839874, 1858594, 1880850, 1950355, 1951650, 1978915, 2044819, 2052899, 2069955, 2085139, 2101779, 2119459, 2133234 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Differs from A341781 at term 3 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.

LINKS

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

EXAMPLE

619090 is a term 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.

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 == 9])

for x in range(len(rets)):

    print(rets[x])

CROSSREFS

Cf. A341891, A341898, A344927, A344945, A345186, A345821.

Sequence in context: A254809 A253818 A341891 * A236064 A204052 A161533

Adjacent sequences:  A341889 A341890 A341891 * A341893 A341894 A341895

KEYWORD

nonn

AUTHOR

David Consiglio, Jr., Jun 04 2021

STATUS

approved

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Last modified December 1 08:44 EST 2021. Contains 349426 sequences. (Running on oeis4.)