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A112643
Odd squarefree abundant numbers.
11
15015, 19635, 21945, 23205, 25935, 26565, 31395, 33495, 33915, 35805, 39585, 41055, 42315, 42735, 45885, 47355, 49665, 50505, 51765, 54285, 55965, 58695, 61215, 64155, 68145, 70455, 72345, 77385, 80535, 82005, 83265, 84315, 91245
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
FORMULA
A087248 INTERSECT A005408.
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
Sequence in context: A104875 A046391 A339938 * A129485 A360526 A249263
KEYWORD
nonn
AUTHOR
Labos Elemer, Sep 20 2005
STATUS
approved