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A047728 Intersection of A046985 and A007691: multiply perfect, refactorable numbers with integer average divisor dividing the number. 1
1, 672, 30240, 23569920, 45532800, 14182439040, 153003540480, 403031236608, 13661860101120, 154345556085770649600, 143573364313605309726720, 352338107624535891640320, 680489641226538823680000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Colton proves (link in A033950) that perfect numbers (A000396) cannot be refactorable.

LINKS

Table of n, a(n) for n=1..13.

FORMULA

All of these four quotients are integers: s1/s0, (x*s0)/s1, s1/x, x/s0.

EXAMPLE

x=45532800, s0=Sigma[ 0,x ]=384, s1=Sigma[ 1,x ]=571963392; Four quotients are all integral: a=s1/s0=474300, b=x/a=96, c=s1/x=4 and q=x/s0=118580.

CROSSREFS

Cf. A000396, A046985, A001599, A007691.

Sequence in context: A234481 A234476 A245782 * A297123 A160209 A234117

Adjacent sequences:  A047725 A047726 A047727 * A047729 A047730 A047731

KEYWORD

nonn

AUTHOR

Labos Elemer

EXTENSIONS

a(7)-a(13) from Donovan Johnson, Apr 09 2010

STATUS

approved

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Last modified November 14 07:07 EST 2019. Contains 329110 sequences. (Running on oeis4.)