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A180935
A180934(n)^a(n) has A180934(n) divisors.
3
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
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
KEYWORD
nonn
AUTHOR
David W. Wilson, Sep 26 2010
STATUS
approved