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A230444 Primes of the form (p^k + k - 1)/k for prime p and some k > 1.

%I A230444 #25 Jun 23 2023 16:56:27
%S A230444 5,13,61,157,181,421,601,733,821,1741,1861,2287,2521,3121,5101,8581,
%T A230444 9661,9931,16381,19609,19801,36721,60901,71821,83641,100801,106261,
%U A230444 135721,161881,163021,199081,205441,218461,273061,282001,337021,388081,431521,491041
%N A230444 Primes of the form (p^k + k - 1)/k for prime p and some k > 1.
%H A230444 Robert Israel, <a href="/A230444/b230444.txt">Table of n, a(n) for n = 1..10000</a>
%e A230444 601 is a term because (7^4 + 4 - 1)/4 = 601 where 7, 601 are both prime,
%e A230444 733 is a term because (13^3 + 3 -1)/3 = 733 where 13, 733 are both prime,
%e A230444 821 is a term because (3^8 + 8 - 1)/8 = 821 where 3, 821 are both prime.
%p A230444 N:= 10^6: # for terms <= N
%p A230444 S:= {}: p:= 1:
%p A230444 do
%p A230444   p:= nextprime(p);
%p A230444   if p^2/2 > N then break fi;
%p A230444   for k from 2 do
%p A230444     v:= (p^k + k - 1)/k;
%p A230444     if v > N then break fi;
%p A230444     if v::integer and isprime(v) then  S:= S union {v} fi;
%p A230444 od od:
%p A230444 sort(convert(S,list)); # _Robert Israel_, Jun 22 2023
%o A230444 (PARI) isA230444(n) = {isprime(n) || return(0); my(k = 2, v, p); while (1, v = k*n+1-k; if (ispower(v, k, &p) && isprime(p), return(1)); if (v < 2^k, return(0)); k++;);} \\ _Michel Marcus_, Oct 19 2013
%Y A230444 Cf. A048161, A067756.
%K A230444 nonn
%O A230444 1,1
%A A230444 _Irina Gerasimova_, Oct 18 2013
%E A230444 More terms from _Michel Marcus_, Oct 19 2013