A341892 Numbers that are the sum of five fourth powers in exactly nine ways.

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

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 =  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
so 619090 is a term.

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