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

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

Offset: 1

Author

Vladimir Shevelev, Feb 28 2011

Keywords

• nonn

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

Examples

			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.
		

Crossrefs

Cf. A186443, A186444, A129657, A000396, A007357.

Programs

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 */

Extensions

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