|
|
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.
|
|
0
|
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|