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%I #21 Jan 20 2020 21:43:14
%S 2,5,7,12,23,24,27,47,58,77,119,121,122,167,238,248,287,340,359,503,
%T 527,621,723,839,959,1014,1328,1367,1679,1847,2037,2180,2194,2207,
%U 2397,2807,3120,3479,3719,4084,4487,4910,5039,5327,6239,6553,6856,6887,7919,8179
%N Numbers of the form p^k - k where p is a prime number and k > 1.
%C Primes of the form p^k - k where p is prime are 2, 5, 7, 23, 47, 167, 359, 503, ...
%C Subsequence of A057897.
%C A182474 is a subsequence.
%C Up to 10^14 all the terms have a unique representation as p^k - k. - _Giovanni Resta_, Mar 21 2017
%H Robert Israel, <a href="/A269769/b269769.txt">Table of n, a(n) for n = 1..10000</a>
%e 2 is a term because 2 = 2^2 - 2.
%e 5 is a term because 5 = 2^3 - 3.
%e 7 is a term because 7 = 3^2 - 2.
%e 12 is a term because 12 = 2^4 - 4.
%e 121 is a term because 121 = 2^7 - 7.
%p N:= 10000: # to get all terms <= N
%p P:= select(isprime, [$1..floor((N+2)^(1/2))]):
%p S:= {}:
%p for k from 2 do
%p pmax:= floor((N+k)^(1/k));
%p if pmax < 2 then break fi;
%p S:= S union {seq(p^k-k, p = select(`<=`,P,pmax))};
%p od:
%p sort(convert(S,list)); # _Robert Israel_, Mar 21 2017
%Y Cf. A000961, A057897, A182474.
%K nonn
%O 1,1
%A _Altug Alkan_, Mar 04 2016
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