%I #8 Apr 06 2020 12:31:29

%S 4,8,9,27,121,125,243,1331,4489,10201,12769,24649,37249,66049,80089,

%T 96721,113569,139129,167281,175561,177147,214369,259081,358801,371293,

%U 413449,426409,436921,552049,579121,591361,635209,823543,1026169

%N Prime powers of prime numbers such that the sum of its digits is also prime power of prime number.

%C Up to 10^7, there are 513 prime powers of prime numbers. Of these, 79 are such that the sum of their digits is also prime power of prime number. Up to 10^14 there are 43915.

%H Robert Israel, <a href="/A076705/b076705.txt">Table of n, a(n) for n = 1..10000</a>

%p N:= 2000000: # for terms <= N

%p R:= NULL:

%p p:= 1:

%p do

%p p:= nextprime(p);

%p if p^2 > N then break fi;

%p q:= 1;

%p do

%p q:= nextprime(q);

%p x:= p^q;

%p if x > N then break fi;

%p R:= R, x;

%p od;

%p od:

%p S:= {R}:

%p sort(convert(select(s -> member(convert(convert(s,base,10),`+`),S),S), list)); # _Robert Israel_, Apr 06 2020

%t pp = Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[10^14]]}, {i, 1, PrimePi[ Floor[ Log[ Prime[n], 10^14]]]}]]]; a = {}; Do[ If[ Position[pp, Plus @@ IntegerDigits[ pp[[n]] ]] != {}, a = Append[a, pp[[n]] ]], {n, 1, 669541}]

%Y Cf. A053810, A075308.

%K nonn,base

%O 1,1

%A _Zak Seidov_, Oct 26 2002

%E Edited and corrected by _Robert G. Wilson v_, Oct 31 2002