A112643 - OEIS

%I #22 Sep 02 2022 04:55:00

%S 15015,19635,21945,23205,25935,26565,31395,33495,33915,35805,39585,

%T 41055,42315,42735,45885,47355,49665,50505,51765,54285,55965,58695,

%U 61215,64155,68145,70455,72345,77385,80535,82005,83265,84315,91245

%N Odd squarefree abundant numbers.

%C Deviates from A046391 (does not contain 36465, 40755 for example).

%C 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

%H Donovan Johnson, <a href="/A112643/b112643.txt">Table of n, a(n) for n = 1..10000</a>

%F A087248 INTERSECT A005408.

%e 199815 = 3 * 5 * 7 * 11 * 173, with 32 divisors adding up to 400896 = 2 * 199815 + 1266.

%p # see A087248 for the additional code

%p isA112643 := proc(n)

%p     isA087248(n) and type(n,'odd') ;

%p end proc:

%p for n from 1 do

%p     if isA112643(n) then

%p         print(n);

%p     end if;

%p end do: # _R. J. Mathar_, Nov 10 2014

%t 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 *)

%t Select[Range[1, 99999, 2], MoebiusMu[#] != 0 && DivisorSigma[1, #] > 2 # &] (* _Alonso del Arte_, Nov 11 2017 *)

%o (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

%Y Cf. A087248, A046391.

%K nonn

%O 1,1

%A _Labos Elemer_, Sep 20 2005