A086454 Number of divisors of prime powers: tau(p^e).

1, 2, 2, 3, 2, 2, 4, 3, 2, 2, 5, 2, 2, 2, 3, 4, 2, 2, 6, 2, 2, 2, 2, 3, 2, 2, 2, 7, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 9, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Reinhard Zumkeller, Jul 20 2003

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Divisor Function.
• Eric Weisstein's World of Mathematics, Prime Power.

Crossrefs

Cf. A000005, A000961, A025474, A086455.

Programs

Mathematica

f[n_] := Module[{f = FactorInteger[n]}, If[Length[f] == 1, f[[1, 2]] + 1, Nothing]]; f[1] = 1; Array[f, 400] (* Amiram Eldar, Apr 09 2024 *)

Formula

a(n) = A000005(A000961(n)).

a(n) = e+1 for A000961(n) = p^e.

a(n) = A025474(n) + 1.