A256603 Numbers D such that D^2 = A^3 + B^4 + C^5 has more than one solution in positive integers (A, B, C).

305, 525, 1206, 1257, 1395, 2048, 2213, 3072, 4348, 6400, 16385, 16640, 16704, 20631, 22872, 23256, 30968, 31407, 32769, 62943, 74515, 77713, 77824, 79776, 82565, 84775, 90432, 98739, 117600, 121250, 133696, 163525, 165628, 171576, 198400, 199872, 243225

Offset: 1

Author

M. F. Hasler, Apr 06 2015

Keywords

• nonn

Comments

A subsequence of A256091. Sequences A256604 and A256652 are the analog for A180241 and A255830.

Examples

			(A, B, C) = (32, 128, 1): 32^3 + 128^4 + 1^5 = 32768 + 268435456 + 1 = 268468225 = 16385^2
(A, B, C) = (1, 128, 8): 1^3 + 128^4 + 8^5 = 1 + 268435456 + 32768 = 268468225 = 16385^2
so 16385 is a term.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..185

Crossrefs

Cf. A180241, A180242, A255830, A256091, A256604, A256613, A256652.

Programs

PARI

for(D=1,9999,f=-1;for(C=1,sqrtn(D^2-1,5),for(B=1,sqrtn(D^2-C^5-.5,4),ispower(D^2-C^5-B^4,3)&&f++&print1(D",")+next(3))))

Extensions

Inserted a(11),a(16) and added a(19)-a(37) by Lars Blomberg, Apr 17 2015