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A286884 Odd numbers n such that the set of distinct prime divisors of n is equal to the set of distinct prime divisors of sum of proper divisors of n. 0
108927, 448335, 544635, 53781261243, 92526188391, 612887145325 (list; graph; refs; listen; history; text; internal format)
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 member 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

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Last modified May 25 11:04 EDT 2019. Contains 323539 sequences. (Running on oeis4.)