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Number of divisors of n which are not greater than the squarefree kernel of n.
5

%I #12 Jul 09 2022 11:09:23

%S 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,

%T 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,

%U 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

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

%H Reinhard Zumkeller, <a href="/A073180/b073180.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) >= A034444(n).

%F a(n) = A095960(n) + 1. - _Reinhard Zumkeller_, Sep 10 2013

%e 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.

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

%o (Haskell)

%o a073180 n = length [x | x <- a027750_row n, x <= a007947 n]

%o -- _Reinhard Zumkeller_, Sep 10 2013

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

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jul 19 2002