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

1,3

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.

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A360458 A074320 A014428 * A151886 A334016 A371241

Adjacent sequences: A180932 A180933 A180934 * A180936 A180937 A180938

Keyword

nonn

Author

David W. Wilson, Sep 26 2010

Status

approved