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A086454
Number of divisors of prime powers: tau(p^e).
1
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
1,2
LINKS
Eric Weisstein's World of Mathematics, Divisor Function.
Eric Weisstein's World of Mathematics, Prime Power.
FORMULA
a(n) = A000005(A000961(n)).
a(n) = e+1 for A000961(n) = p^e.
a(n) = A025474(n) + 1.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 20 2003
STATUS
approved