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

1,1

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

Links

Table of n, a(n) for n=1..6.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A237789 A157533 A233650 * A210083 A238044 A237963

Adjacent sequences: A286881 A286882 A286883 * A286885 A286886 A286887

Keyword

nonn,more

Author

Altug Alkan, Aug 02 2017

Extensions

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

Status

approved