The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #10 Apr 09 2024 08:09:36
%S 1,1,2,4,6,4,10,12,16,18,22,12,3,28,30,36,3,40,42,4,46,24,52,58,60,66,
%T 70,72,78,20,82,88,96,100,102,106,108,112,60,126,130,136,138,148,150,
%U 8,156,162,166,84,172,178,180,190,192,196,198,210,222,7,226,228,232,238
%N A180934(n)^a(n) has A180934(n) divisors.
%C For n > 1, a(n) gives the unique solution k of d(m^k) = m where d = A000005. For m = 1, any integer k will do, we choose the smallest positive solution a(1) = 1.
%C For prime p, p-1 is in this sequence.
%C For odd semiprime s, (s-1)/2 is in this sequence.
%H David W. Wilson, <a href="/A180935/b180935.txt">Table of n, a(n) for n=1..10000</a>
%e 11^10 has 11 divisors, so a(n) = 10 where A180934(n) = 11.
%e 225^7 has 225 divisors, so a(n) = 7 where A180934(n) = 225.
%t f[n_] := Module[{e = FactorInteger[n][[;; , 2]], k = 1}, While[n > Times @@ (k*e + 1), k++]; If[n == Times @@ (k*e + 1), k, Nothing]]; f[1] = 1; Array[f, 250] (* _Amiram Eldar_, Apr 09 2024 *)
%Y Cf. A000005, A006093, A046315, A180934, A180936.
%K nonn
%O 1,3
%A _David W. Wilson_, Sep 26 2010