%I #34 Mar 13 2020 17:49:25

%S 9,1331,357911,5177717,5735339,9393931,17171515157399,335571975137771,

%T 7979737131773191,13337513771953951,13137917533317175739371379,

%U 33159599371999557199755557,1593395573971551557179777111133,131755773357537951113179771515713,315113377779977515359339551539771

%N Numbers k of the form p^q where both p and q are prime and all digits of k are odd.

%C Up to 10^17, there are only 10 odd-digit prime powers of prime numbers. a(1) = 3^2, a(2) = 11^3, a(3) = 71^3, a(4) = 173^3, a(5) = 179^3, a(6) = 211^3, a(7) = 25799^3, a(8) = 69491^3, a(9) = 199831^3, and a(10) = 237151^3.

%C The only candidates for even-digit prime powers of prime numbers are of the form 2^n, and below 2^10000 there are only 2, 4, 8, 64, and 2048, two of which are not raised to prime powers.

%C a(11) <= 13137917533317175739371379 and a(12) <= 33159599371999557199755557. - _Jinyuan Wang_, Mar 02 2020

%H Giovanni Resta, <a href="/A076704/b076704.txt">Table of n, a(n) for n = 1..36</a> (terms < 10^57)

%t pp = Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[10^17]]}, {i, 1, PrimePi[ Floor[ Log[ Prime[n], 10^17]]]}]]]; Do[ If[ Union[ OddQ[ IntegerDigits[ pp[[n]]]]] == {True}, Print[ pp[[n]]]], {n, 1, Length[pp]}]

%o (PARI) lista(nn) = {my(k, v=List([])); forprime(p=2, nn, forprime(q=2, logint(nn, p), if(Set(digits(k=p^q)%2)==[1], listput(v, k)))); Set(v); } \\ _Jinyuan Wang_, Mar 02 2020

%Y Cf. A014261, A053810, A075308.

%K nonn,base

%O 1,1

%A _Zak Seidov_, Oct 26 2002

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

%E Corrected and edited by _Elliott Line_, Jul 11 2013

%E Better definition from _Jon E. Schoenfield_, Nov 19 2018

%E Terms a(11) and beyond from _Giovanni Resta_, Mar 03 2020