A344278 Numbers that are the sum of three fourth powers in exactly four ways.

5978882, 15916082, 20621042, 22673378, 30623138, 33998258, 39765362, 48432482, 53809938, 61627202, 65413922, 74346818, 84942578, 88258898, 95662112, 103363442, 117259298, 128929682, 131641538, 137149922, 143244738, 155831858, 158811842, 167042642, 174135122, 175706258, 188529362

Offset: 1

Author

David Consiglio, Jr., May 13 2021

Keywords

• nonn

Comments

Differs from A344277 at term 37 because 292965218 = 2^4 + 109^4 + 111^4 = 21^4 + 98^4 + 119^4 = 27^4 + 94^4 + 121^4 = 34^4 + 89^4 + 123^4 = 49^4 + 77^4 + 126^4 = 61^4 + 66^4 + 127^4

Examples

			20621042 is a member of this sequence because 20621042 = 5^4 + 54^4 + 59^4 = 10^4 + 51^4 + 61^4 = 25^4 + 46^4 + 63^4 = 26^4 + 39^4 + 65^4
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 1..7946

Crossrefs

Cf. A343969, A344240, A344277, A344353, A344365.

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(1,50)]
for pos in cwr(power_terms,3):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v == 4])
for x in range(len(rets)):
    print(rets[x])