A073183 Sum of divisors of n that are not greater than the cubefree kernel of n.
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, 42, 13, 56, 30, 72, 32, 7, 48, 54, 48, 91, 38, 60, 56, 50, 42, 96, 44, 84, 78, 72, 48, 36, 57, 93, 72, 98, 54, 39, 72, 64, 80, 90, 60, 168, 62, 96, 104, 7, 84, 144, 68, 126, 96, 144, 72
Offset: 1
Examples
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.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
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 *) -
PARI
a007948(n) = my(f=factor(n)); for (i=1, #f~, f[i, 2] = min(f[i, 2], 2)); factorback(f); a(n) = sumdiv(n, d, d*(d<=a007948(n))); \\ Michel Marcus, Feb 07 2015
Comments