%I #7 Aug 23 2017 06:06:35

%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,2,1,1,1,2,2,1,1,1,1,2,1,1,2,1,

%T 3,1,1,1,3,1,1,1,1,2,3,1,1,1,1,2,3,3,1,1,1,3,1,1,1,1,1,1,1,3,2,2,1,3,

%U 2,3,1,3,1,1,1,1,1,3,1,3,2,1,1,3,3,1,2,1,1,3,1,2,1,1,1,3,1,1,1,1,1,3,1,2,2

%N a(n) = the least natural number k such that k*phi(n) + 1 is prime.

%H Antti Karttunen, <a href="/A072344/b072344.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A034693(A000010(n)). - _Antti Karttunen_, Aug 22 2017

%e phi(35) = 24 and the least natural number k such that 24 k + 1 is prime is k = 3; so a(35) = 3.

%t f[n_] := Module[{i}, i = 0; While[ ! PrimeQ[i*EulerPhi[n] + 1], i++ ]; i]; Table[f[i], {i, 1, 150}]

%o (PARI)

%o A034693(n) = { my(k=1); while(!isprime(1+(k*n)), k++); k; };

%o A072344(n) = A034693(eulerphi(n)); \\ _Antti Karttunen_, Aug 22 2017

%Y Cf. A000010, A034693, A072917.

%K nonn

%O 1,15

%A _Joseph L. Pe_, Jul 16 2002