A286884 - OEIS

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 (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 term because sigma(92526188391) - 92526188391 = 3^2713^319181^2 and 92526188391 = 3^27^213^219^3181.`
	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`

Last modified February 8 07:51 EST 2023. Contains 360136 sequences. (Running on oeis4.)