A180935 A180934(n)^a(n) has A180934(n) divisors.

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, 70, 72, 78, 20, 82, 88, 96, 100, 102, 106, 108, 112, 60, 126, 130, 136, 138, 148, 150, 8, 156, 162, 166, 84, 172, 178, 180, 190, 192, 196, 198, 210, 222, 7, 226, 228, 232, 238

Offset: 1

Author

David W. Wilson, Sep 26 2010

Keywords

• nonn

Comments

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.

For prime p, p-1 is in this sequence.

For odd semiprime s, (s-1)/2 is in this sequence.

Examples

			11^10 has 11 divisors, so a(n) = 10 where A180934(n) = 11.
225^7 has 225 divisors, so a(n) = 7 where A180934(n) = 225.
		

Links

• David W. Wilson, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A000005, A006093, A046315, A180934, A180936.

Programs

Mathematica

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 *)