A286884 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.

108927, 448335, 544635, 53781261243, 92526188391, 612887145325

Offset: 1

Author

Altug Alkan, Aug 02 2017

Keywords

• nonn
• more

Comments

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

Examples

			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.
		

Crossrefs

Cf. A001065, A007947, A027598, A027748, A286876.

Programs

Mathematica

fQ[n_] := Transpose[ FactorInteger[ n]][[1]] == Transpose[ FactorInteger[ DivisorSigma[1, n] - n]][[1]];  (* Robert G. Wilson v, Aug 02 2017 *)

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

Extensions

a(4)-a(6) from Giovanni Resta, Aug 03 2017