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

Author

David Consiglio, Jr., Jun 04 2021

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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])