A073180 Number of divisors of n which are not greater than the squarefree kernel of n.

1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 5, 2, 4, 4, 2, 2, 4, 2, 5, 4, 4, 2, 5, 2, 4, 2, 5, 2, 8, 2, 2, 4, 4, 4, 5, 2, 4, 4, 6, 2, 8, 2, 5, 5, 4, 2, 5, 2, 4, 4, 5, 2, 4, 4, 6, 4, 4, 2, 11, 2, 4, 5, 2, 4, 8, 2, 5, 4, 8, 2, 5, 2, 4, 4, 5, 4, 8, 2, 6, 2, 4, 2, 11, 4, 4, 4, 6, 2, 10, 4, 5, 4, 4, 4, 5, 2, 4, 5, 5, 2, 8, 2

Offset: 1

Author

Reinhard Zumkeller, Jul 19 2002

Keywords

• nonn

Examples

			The squarefree kernel of 56 = 7*2^3 is 14 = 7*2 and the divisors <= 14 of 56 are {1, 2, 4, 7, 8, 14}, therefore a(56) = 6.
		

Links

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

Crossrefs

Cf. A000005, A007947, A034444, A073181, A073182, A095960.

Programs

Haskell

a073180 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(n) >= A034444(n).

a(n) = A095960(n) + 1. - Reinhard Zumkeller, Sep 10 2013