A086416 Number of divisors of 3-smooth numbers.

1, 2, 2, 3, 4, 4, 3, 6, 5, 6, 8, 4, 6, 9, 10, 8, 7, 12, 5, 12, 12, 8, 15, 10, 14, 16, 6, 9, 18, 15, 16, 20, 12, 10, 21, 20, 7, 18, 24, 18, 11, 24, 25, 14, 20, 28, 24, 12, 8, 27, 30, 21, 22, 32, 30, 13, 16, 30, 35, 28, 24, 9, 36, 36, 14, 24, 33, 40, 35, 26, 18, 40, 42, 15, 32

Offset: 1

Author

Reinhard Zumkeller, Jul 18 2003

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A086414, A086415, A086417.

Cf. A000005, A003586, A022328, A022329.

Programs

Mathematica

DivisorSigma[0, Select[Range[10000], # == 2^IntegerExponent[#, 2] * 3^IntegerExponent[#, 3] &]] (* Amiram Eldar, Apr 15 2024 *)

Formula

a(n) = A000005(A003586(n)).

a(n) = if A086414(n) = A086415(n) then A086414(n)+1 else (A086414(n)+1)*(A086415(n)+1).

a(n) = (A022328(n)+1)*(A022329(n)+1).