

A186889


Oex perfect numbers: n such that A186644(n) = 2*n.


0




OFFSET

1,1


COMMENTS

There are no squarefree infinitary perfect numbers > 6 (cf. A007357). Therefore, the second and all further terms of the sequence are infinitary deficient (A129657).
No further term between 1888 and 1440000.  R. J. Mathar, Mar 18 2011
a(11) > 3*10^10. 1471763808896 is also a term.  Donovan Johnson, Jan 30 2013


LINKS

Table of n, a(n) for n=1..10.


EXAMPLE

Let n = 100 with divisors 1, 2, 4, 5, 10, 20, 25, 50, and 100. By the definition in A186643, only 1, 4, 20, 25, 50, 100 among these are oex divisors. Since 1+4+20+25+50+100 = 2*100, 100 is in the sequence.


PROG

(PARI) for(n=4, 10^9, if(isprime(n), next); d=divisors(n); s=n+1; for(j=2, numdiv(n)1, for(k=2, 30, if(n%d[j]^k<>0, if(k%2==0, s=s+d[j]); k=30))); if(s==2*n, print(n))) /* Donovan Johnson, Jan 28 2013 */


CROSSREFS

Cf. A186443, A186444, A129657, A000396, A007357.
Sequence in context: A107405 A077663 A025163 * A022418 A081318 A275168
Adjacent sequences: A186886 A186887 A186888 * A186890 A186891 A186892


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Feb 28 2011


EXTENSIONS

a(6)a(10) from Donovan Johnson, Jan 28 2013


STATUS

approved



