A095960 Number of divisors of n that are less than the squarefree kernel of n.

0, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 4, 1, 3, 3, 1, 1, 3, 1, 4, 3, 3, 1, 4, 1, 3, 1, 4, 1, 7, 1, 1, 3, 3, 3, 4, 1, 3, 3, 5, 1, 7, 1, 4, 4, 3, 1, 4, 1, 3, 3, 4, 1, 3, 3, 5, 3, 3, 1, 10, 1, 3, 4, 1, 3, 7, 1, 4, 3, 7, 1, 4, 1, 3, 3, 4, 3, 7, 1, 5, 1, 3, 1, 10, 3, 3, 3, 5, 1, 9, 3, 4, 3, 3, 3, 4, 1, 3, 4, 4, 1, 7

Offset: 1

Author

Reinhard Zumkeller, Jul 14 2004

Keywords

• nonn

Examples

			n = 40 = 5*2^3, rad(40) = 10: a(40) = #{d:d<10} = #{1,2,4,5,8} = 5.
		

Links

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

Crossrefs

Cf. A000005, A000040, A005117, A007947, A027750, A032741, A073180.

Programs

Haskell

a095960 n = length [x | x <- a027750_row n, x < a007947 n]
-- Reinhard Zumkeller, Sep 10 2013

Mathematica

a[n_] := DivisorSum[n, 1 &, # < Times @@ FactorInteger[n][[;;, 1]] &]; Array[a, 100] (* Amiram Eldar, Jul 09 2022 *)

Formula

a(A005117(n)) = A032741(A005117(n)).

a(A000040(n)) = 1.