

A255830


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


7



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
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OFFSET

1,1


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.


LINKS

Table of n, a(n) for n=1..50.


EXAMPLE

(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.


PROG

(PARI) is_A255830(D)=my(B, C=0, D2C6); while(1<D2C6=D^2C++^6, B=0; while(0<D2C6B++^5, ispower(D^2C^6B^5, 4)&&return(1)))
for(D=1, 9999, is_A255830(D)&&print1(D", ")) \\ Converted to integer arithmetic by M. F. Hasler, May 01 2015


CROSSREFS

Cf. A256091, A256613, A180241, A180242, A256652.
Sequence in context: A022321 A194830 A183344 * A256613 A116484 A138749
Adjacent sequences: A255827 A255828 A255829 * A255831 A255832 A255833


KEYWORD

nonn


AUTHOR

M. F. Hasler, Apr 06 2015


EXTENSIONS

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


STATUS

approved



