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%I #27 Jul 22 2021 23:48:08
%S 108927,448335,544635,53781261243,92526188391,612887145325
%N Odd numbers k such that the set of distinct prime divisors of k is equal to the set of distinct prime divisors of the sum of proper divisors of k.
%C The first four terms that are divisible by 108927 are 108927, 544635, 92526188391, 4094089374375.
%C a(7) > 10^12. 2981095241355 is also a term. - _Giovanni Resta_, Aug 03 2017
%e 92526188391 is a term because sigma(92526188391) - 92526188391 = 3^2*7*13^3*19*181^2 and 92526188391 = 3^2*7^2*13^2*19^3*181.
%t fQ[n_] := Transpose[ FactorInteger[ n]][[1]] == Transpose[ FactorInteger[ DivisorSigma[1, n] - n]][[1]]; (* _Robert G. Wilson v_, Aug 02 2017 *)
%o (PARI) a001065(n) = if(n==0, 0, sigma(n) - n)
%o a027748(n) = factor(n)[, 1]~
%o is(n) = n%2==1 && a027748(n)==a027748(a001065(n)) \\ _Felix Fröhlich_, Aug 02 2017
%o (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
%Y Cf. A001065, A007947, A027598, A027748, A286876.
%K nonn,more
%O 1,1
%A _Altug Alkan_, Aug 02 2017
%E a(4)-a(6) from _Giovanni Resta_, Aug 03 2017
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