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

1,1

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A077502 A297415 A346526 * A265505 A162305 A029773

Adjacent sequences: A282547 A282548 A282549 * A282551 A282552 A282553

Keyword

nonn

Author

Altug Alkan, Feb 18 2017

Extensions

More terms from Felix Fröhlich, Feb 18 2017

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

Status

approved