

A073183


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


5



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
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OFFSET

1,2


COMMENTS

a(n) >= A073185(n).


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000


EXAMPLE

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.


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 *)


PROG

(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


CROSSREFS

Cf. A000203, A007948, A073182, A073181.
Sequence in context: A113957 A073185 A284341 * A049418 A051378 A254981
Adjacent sequences: A073180 A073181 A073182 * A073184 A073185 A073186


KEYWORD

nonn,look


AUTHOR

Reinhard Zumkeller, Jul 19 2002


STATUS

approved



