A344927 Numbers that are the sum of four fourth powers in exactly nine ways.

328118259, 385202034, 395613234, 489597858, 625839858, 641398338, 674511618, 693239634, 699598578, 722302434, 779889314, 780278643, 782999714, 791204514, 792005379, 797405714, 797935698, 805299699, 815120658, 822938754, 851527314, 857962914, 870861618

Offset: 1

Author

David Consiglio, Jr., Jun 02 2021

Keywords

• nonn

Comments

Differs from A344926 at term 5 because 328118259 is a term because 328118259 = 2^4 + 77^4 + 109^4 + 111^4 = 8^4 + 79^4 + 93^4 + 121^4 = 18^4 + 79^4 + 97^4 + 119^4 = 21^4 + 77^4 + 98^4 + 119^4 = 27^4 + 77^4 + 94^4 + 121^4 = 34^4 + 77^4 + 89^4 + 123^4 = 46^4 + 57^4 + 103^4 + 119^4 = 49^4 + 77^4 + 77^4 + 126^4 = 61^4 + 66^4 + 77^4 + 127^4.

Examples

			328118259 is a term because 328118259 = 2^4 + 77^4 + 109^4 + 111^4  = 8^4 + 79^4 + 93^4 + 121^4  = 18^4 + 79^4 + 97^4 + 119^4  = 21^4 + 77^4 + 98^4 + 119^4  = 27^4 + 77^4 + 94^4 + 121^4  = 34^4 + 77^4 + 89^4 + 123^4  = 46^4 + 57^4 + 103^4 + 119^4  = 49^4 + 77^4 + 77^4 + 126^4  = 61^4 + 66^4 + 77^4 + 127^4.
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 1..64

Crossrefs

Cf. A341892, A344751, A344925, A344926, A344929, A345154.

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, 4):
    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])