OFFSET
1,1
COMMENTS
Deviates from A046391 (does not contain 36465, 40755 for example).
The numbers of terms not exceeding 10^k, for k = 5, 6, ..., are 34, 134, 1663, 16328, 175630, 1694621, 16726454, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00016... . - Amiram Eldar, Sep 02 2022
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..10000
EXAMPLE
199815 = 3 * 5 * 7 * 11 * 173, with 32 divisors adding up to 400896 = 2 * 199815 + 1266.
MAPLE
# see A087248 for the additional code
isA112643 := proc(n)
isA087248(n) and type(n, 'odd') ;
end proc:
for n from 1 do
if isA112643(n) then
print(n);
end if;
end do: # R. J. Mathar, Nov 10 2014
MATHEMATICA
ta = {{0}}; Do[g = n; s = DivisorSigma[1, n] - 2 * n; If[Greater[s, 0] && Equal[Abs[MoebiusMu[n]], 1] && !Equal[Mod[n, 2], 0], Print[n, PrimeFactorList[n], s]; ta = Append[ta, n]], {n, 1, 200000}]; {ta = Delete[ta, 1], g}(* Elemer *)
Select[Range[1, 99999, 2], MoebiusMu[#] != 0 && DivisorSigma[1, #] > 2 # &] (* Alonso del Arte, Nov 11 2017 *)
PROG
(PARI) is(n)=if(n%2==0, return(0)); my(f=factor(n)); sigma(f)>2*n && vecmax(f[, 2])==1 \\ Charles R Greathouse IV, Feb 21 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Sep 20 2005
STATUS
approved