A282550 Perfect powers that are the sum of two distinct proper prime powers (A246547).

25, 36, 81, 125, 144, 196, 324, 512, 576, 1089, 2304, 2744, 2916, 5041, 9216, 14884, 16641, 26244, 36864, 51984, 147456, 236196, 589824, 941192, 1196836, 2125764, 2359296, 9437184, 19131876, 37748736, 67125249, 150994944, 172186884, 322828856, 603979776

Offset: 1

Author

Altug Alkan, Feb 18 2017

Keywords

• nonn

Comments

Intersection of A001597 and A225102. - Michel Marcus, Feb 18 2017

Terms t of A001597 such that A225099(t) > 0. - Felix Fröhlich, Feb 18 2017

Examples

			512 = 2^9 is a term because 2^9 = 7^3 + 13^2.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..45 (terms < 2*10^11)

Crossrefs

Cf. A001597, A225099, A225102, A225106, A246547.

Programs

Mathematica

Select[Union@ Map[Total, Subsets[With[{nn = 10^6}, Complement[ Select[ Range@ nn, PrimePowerQ], Prime[Range[PrimePi@ nn]]]], {2}]], # == 1 ||
GCD @@ FactorInteger[#][[All, 2]] > 1 &] (* Michael De Vlieger, Feb 18 2017, after Harvey P. Dale at A246547 *)

PARI

is(n) = if(!ispower(n), return(0), my(x=n-1, y=1); while(y < x, if(isprimepower(x) && isprimepower(y) && !ispseudoprime(x) && !ispseudoprime(y), return(1)); y++; x--)); 0 \\ Felix Fröhlich, Feb 18 2017

Extensions

More terms from Felix Fröhlich, Feb 18 2017

a(28)-a(35) from Giovanni Resta, May 07 2017