A341898 Numbers that are the sum of five fourth powers in exactly ten ways.

954979, 1205539, 1574850, 1713859, 1863859, 1877394, 1882579, 2071939, 2109730, 2225859, 2288179, 2419954, 2492434, 2495939, 2605314, 2711394, 2784499, 2835939, 2847394, 2880994, 2924674, 3007474, 3061939, 3071379, 3074179, 3117235, 3127219, 3174834, 3190899

Offset: 1

Author

David Consiglio, Jr., Jun 04 2021

Keywords

• nonn

Comments

Differs at term 5 because

1801459 = 1^4 + 4^4 + 5^4 + 28^4 + 33^4

= 1^4 + 4^4 + 12^4 + 23^4 + 35^4

= 1^4 + 7^4 + 16^4 + 30^4 + 31^4

= 1^4 + 16^4 + 18^4 + 19^4 + 35^4

= 3^4 + 6^4 + 18^4 + 21^4 + 35^4

= 5^4 + 7^4 + 19^4 + 24^4 + 34^4

= 5^4 + 9^4 + 14^4 + 29^4 + 32^4

= 7^4 + 9^4 + 16^4 + 25^4 + 34^4

= 7^4 + 14^4 + 16^4 + 21^4 + 35^4

= 8^4 + 9^4 + 20^4 + 29^4 + 31^4

= 10^4 + 19^4 + 19^4 + 21^4 + 34^4.

Examples

			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
so 954979 is a term.
		

Links

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

Crossrefs

Cf. A341892, A341897, A344929, A345188, A345822.

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 == 10])
for x in range(len(rets)):
    print(rets[x])