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COMMENTS
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The first four terms that are divisible by 108927 are 108927, 544635, 92526188391, 4094089374375.
a(7) > 10^12. 2981095241355 is also a term. - Giovanni Resta, Aug 03 2017
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PROG
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(PARI) a001065(n) = if(n==0, 0, sigma(n) - n)
a027748(n) = factor(n)[, 1]~
is(n) = n%2==1 && a027748(n)==a027748(a001065(n)) \\ Felix Fröhlich, Aug 02 2017
(PARI) list(lim)=my(v=List(), f, t, o); forfactored(n=108927, lim\1, f=n[2]; if(f[1, 1]==2, next); t=sigma(f)-n[1]; for(i=1, #f~, o=valuation(t, f[i, 1]); if(o==0, next(2)); t/=f[i, 1]^o); if(t==1, listput(v, n[1]))); Vec(v) \\ Charles R Greathouse IV, Aug 02 2017
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