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A112643 Odd squarefree abundant numbers. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..10000

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

Cf. A087248, A046391.

Sequence in context: A165614 A104875 A046391 * A129485 A249263 A294026

Adjacent sequences:  A112640 A112641 A112642 * A112644 A112645 A112646

KEYWORD

nonn

AUTHOR

Labos Elemer, Sep 20 2005

STATUS

approved

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Last modified November 14 19:12 EST 2018. Contains 317214 sequences. (Running on oeis4.)