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Sum of divisors of n that are not greater than the cubefree kernel of n.
5

%I #20 Jul 14 2018 18:33:06

%S 1,3,4,7,6,12,8,7,13,18,12,28,14,24,24,7,18,39,20,42,32,36,24,36,31,

%T 42,13,56,30,72,32,7,48,54,48,91,38,60,56,50,42,96,44,84,78,72,48,36,

%U 57,93,72,98,54,39,72,64,80,90,60,168,62,96,104,7,84,144,68,126,96,144,72

%N Sum of divisors of n that are not greater than the cubefree kernel of n.

%C a(n) >= A073185(n).

%H Antti Karttunen, <a href="/A073183/b073183.txt">Table of n, a(n) for n = 1..10000</a>

%e The cubefree kernel of 56 = 7 * 2^3 is 28 = 7 * 2^2 and the divisors <= 28 of 56 are {1, 2, 4, 7, 8, 14, 28}, therefore a(56) = 1 + 2 + 4 + 7 + 8 + 14 + 28 = 64.

%t sdcfk[n_]:=Module[{cf=Times@@Flatten[Table[#[[1]],#[[2]]]&/@({#[[1]],If[ #[[2]]>2,2,#[[2]]]}&/@FactorInteger[n])]},Total[Select[Divisors[n],#<= cf&]]]; Array[sdcfk,80] (* _Harvey P. Dale_, Jul 14 2018 *)

%o (PARI) a007948(n) = my(f=factor(n)); for (i=1, #f~, f[i, 2] = min(f[i, 2], 2)); factorback(f);

%o a(n) = sumdiv(n, d, d*(d<=a007948(n))); \\ _Michel Marcus_, Feb 07 2015

%Y Cf. A000203, A007948, A073182, A073181.

%K nonn,look

%O 1,2

%A _Reinhard Zumkeller_, Jul 19 2002