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%I #7 Apr 30 2024 01:47:04
%S 1,2,3,4,652245
%N Numbers k such that prime(k) = d(k)*phi(k) + 1, where d(k) is number of positive divisors of k.
%C There is no further term up to 5*10^7.
%C a(6) > 10^10, if it exists. - _Amiram Eldar_, Apr 30 2024
%e 652245 is in the sequence because prime(652245) = d(652245)*phi(652245) + 1.
%t Do[If[Prime[n] == DivisorSigma[0, n]*EulerPhi[n] + 1, Print[n]], {n, 50000000}]
%o (PARI) lista(pmax) = {my(k = 0, f); forprime(p=1, 1e16, k++; f = factor(k); if(p == numdiv(f)*eulerphi(f)+1, print1(k,", ")));} \\ _Amiram Eldar_, Apr 30 2024
%Y Cf. A000005, A000010, A104905, A107657.
%K nonn,more
%O 1,2
%A _Farideh Firoozbakht_, Jun 06 2005
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