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A073181 Sum of divisors of n which are not greater than the squarefree kernel of n.

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%I A073181 #14 Jul 09 2022 11:09:27
%S A073181 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 A073181 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 A073181 72,46,54,12,72,36,80,90,60,108,62,96,41,3,84,144,68,58,96,144,72,16,74
%N A073181 Sum of divisors of n which are not greater than the squarefree kernel of n.
%H A073181 Antti Karttunen, <a href="/A073181/b073181.txt">Table of n, a(n) for n = 1..10000</a>
%F A073181 a(n) >= A048250(n).
%e A073181 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 A073181 a[n_] := DivisorSum[n, # &, # <= Times @@ FactorInteger[n][[;;, 1]] &]; Array[a, 100] (* _Amiram Eldar_, Jul 09 2022 *)
%o A073181 (PARI)
%o A073181 A007947(n) = factorback(factorint(n)[, 1]); \\ This function from _Andrew Lelechenko_
%o A073181 A073181(n) = sumdiv(n, d, d*(d<=A007947(n))); \\ _Antti Karttunen_, Sep 10 2017, after _Michel Marcus_'s code for A073183.
%Y A073181 Cf. A000203, A007947, A048250, A073180, A073183.
%K A073181 nonn,look
%O A073181 1,2
%A A073181 _Reinhard Zumkeller_, Jul 19 2002