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

1,6

Links

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

Formula

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

a(A000040(n)) = 1.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A102396 A344852 A372720 * A316314 A183093 A183096

Adjacent sequences: A095957 A095958 A095959 * A095961 A095962 A095963

Keyword

nonn

Author

Reinhard Zumkeller, Jul 14 2004

Status

approved