A282550 - OEIS

%I #26 May 07 2017 13:21:06

%S 25,36,81,125,144,196,324,512,576,1089,2304,2744,2916,5041,9216,14884,

%T 16641,26244,36864,51984,147456,236196,589824,941192,1196836,2125764,

%U 2359296,9437184,19131876,37748736,67125249,150994944,172186884,322828856,603979776

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

%C Intersection of A001597 and A225102. - _Michel Marcus_, Feb 18 2017

%C Terms t of A001597 such that A225099(t) > 0. - _Felix Fröhlich_, Feb 18 2017

%H Giovanni Resta, <a href="/A282550/b282550.txt">Table of n, a(n) for n = 1..45</a> (terms < 2*10^11)

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

%t Select[Union@ Map[Total, Subsets[With[{nn = 10^6}, Complement[ Select[ Range@ nn, PrimePowerQ], Prime[Range[PrimePi@ nn]]]], {2}]], # == 1 ||

%t GCD @@ FactorInteger[#][[All, 2]] > 1 &] (* _Michael De Vlieger_, Feb 18 2017, after _Harvey P. Dale_ at A246547 *)

%o (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

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

%K nonn

%O 1,1

%A _Altug Alkan_, Feb 18 2017

%E More terms from _Felix Fröhlich_, Feb 18 2017

%E a(28)-a(35) from _Giovanni Resta_, May 07 2017