A047728 Intersection of A046985 and A007691: multiply perfect, refactorable numbers with integer average divisor dividing the number.

1, 672, 30240, 23569920, 45532800, 14182439040, 153003540480, 403031236608, 13661860101120, 154345556085770649600, 143573364313605309726720, 352338107624535891640320, 680489641226538823680000

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: A340864 A331666 A245782 * A297123 A335254 A160209

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