A186889 Oex perfect numbers: n such that A186644(n) = 2*n.

6, 18, 20, 100, 1888, 2044928, 33099776, 35021696, 45335936, 533020672

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: A372438 A077663 A025163 * A022418 A350848 A373413

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