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A095960 Number of divisors of n that are less than the squarefree kernel of n. 2

%I #15 Jul 09 2022 11:09:09

%S 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,

%T 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,

%U 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

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

%H Reinhard Zumkeller, <a href="/A095960/b095960.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(A000040(n)) = 1.

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

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

%o (Haskell)

%o a095960 n = length [x | x <- a027750_row n, x < a007947 n]

%o -- _Reinhard Zumkeller_, Sep 10 2013

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

%K nonn

%O 1,6

%A _Reinhard Zumkeller_, Jul 14 2004

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Last modified April 19 15:34 EDT 2024. Contains 371794 sequences. (Running on oeis4.)