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Sum of divisors of n which are not greater than the squarefree kernel of n.
4

%I #14 Jul 09 2022 11:09:27

%S 1,3,4,3,6,12,8,3,4,18,12,16,14,24,24,3,18,12,20,22,32,36,24,16,6,42,

%T 4,28,30,72,32,3,48,54,48,16,38,60,56,30,42,96,44,40,33,72,48,16,8,18,

%U 72,46,54,12,72,36,80,90,60,108,62,96,41,3,84,144,68,58,96,144,72,16,74

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

%H Antti Karttunen, <a href="/A073181/b073181.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) >= A048250(n).

%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) = 1 + 2 + 4 + 7 + 8 + 14 = 36.

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

%o (PARI)

%o A007947(n) = factorback(factorint(n)[, 1]); \\ This function from _Andrew Lelechenko_

%o A073181(n) = sumdiv(n, d, d*(d<=A007947(n))); \\ _Antti Karttunen_, Sep 10 2017, after _Michel Marcus_'s code for A073183.

%Y Cf. A000203, A007947, A048250, A073180, A073183.

%K nonn,look

%O 1,2

%A _Reinhard Zumkeller_, Jul 19 2002