A088244 Number of 3-smooth divisors of n!.

1, 1, 2, 4, 8, 8, 15, 15, 24, 40, 45, 45, 66, 66, 72, 84, 112, 112, 153, 153, 171, 190, 200, 200, 253, 253, 264, 336, 364, 364, 405, 405, 480, 512, 528, 528, 630, 630, 648, 684, 741, 741, 800, 800, 840, 924, 946, 946, 1081, 1081, 1104, 1152, 1200, 1200

Offset: 0

Author

Reinhard Zumkeller, Jan 23 2004

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000005, A003586.

Cf. A000142, A072078.

Cf. A011371, A054861.

Programs

Mathematica

a[n_] := ((1 + IntegerExponent[n!, 2])*(1 + IntegerExponent[n!, 3])); Array[a, 100, 0] (* Amiram Eldar, Aug 30 2019 *)

Formula

a(n) = A072078(A000142(n)).

a(n) = a(n-1) iff gcd(n,6) = 1.

a(n) = (A011371(n)+1)*(A054861(n)+1).