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A186889
Oex perfect numbers: n such that A186644(n) = 2*n.
0
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
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
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Feb 28 2011
EXTENSIONS
a(6)-a(10) from Donovan Johnson, Jan 28 2013
STATUS
approved