A255830 Numbers D such that D^2 = A^4 + B^5 + C^6 for some positive integers A, B, C.

7, 9, 17, 33, 72, 89, 96, 99, 105, 137, 171, 213, 218, 240, 320, 459, 503, 513, 525, 616, 761, 792, 833, 1048, 1127, 1257, 1369, 1395, 1536, 1551, 2025, 2457, 2600, 2610, 3267, 3312, 3600, 3681, 4032, 4100, 4125, 4128, 4201, 4901, 4976, 5001, 5225, 5880, 5975, 6167

Offset: 1

Author

M. F. Hasler, Apr 06 2015

Keywords

• nonn

Comments

The sequence has the infinite subsequence (4^n*(2^n+16), n=0,1,2,...), with corresponding (A,B,C) = (2^(n+2),2^(n+1),2^n).

See A256652 for terms whose square has more than one representation of the given form. See A256613 for the subsequence of terms such that A^2 + B^3 + C^4 is a square, cf. A180241. See A256091 for the analog for sums of 3rd, 4th and 5th power.

Examples

			(A, B, C) = (1, 4, 2) = 1^4 + 4^5 + 2^6 = 1 + 1024 + 64 = 1089 = 33^2, so 33 is a term.
(A, B, C) = (1, 4, 8) = 1^4 + 4^5 + 8^6 = 1 + 1024 + 262144 = 263169 = 513^2, so 513 is a term.
		

Crossrefs

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

Programs

PARI

is_A255830(D)=my(B,C=0,D2C6); while(1A255830(D)&&print1(D",")) \\ Converted to integer arithmetic by M. F. Hasler, May 01 2015

Extensions

Inserted a(4)=33, a(18)=513 and removed doublet 1257 by Lars Blomberg, Apr 26 2015