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

1,2

Links

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

Formula

a(n) >= A034444(n).

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

Example

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.

Mathematica

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

Prog

(Haskell)
a073180 n = length [x | x <- a027750_row n, x <= a007947 n]
-- Reinhard Zumkeller, Sep 10 2013

Crossrefs

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

Sequence in context: A365171 A369310 A318465 * A316398 A183095 A304817

Adjacent sequences: A073177 A073178 A073179 * A073181 A073182 A073183

Keyword

nonn

Author

Reinhard Zumkeller, Jul 19 2002

Status

approved