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A087248 Squarefree abundant numbers. 7
30, 42, 66, 70, 78, 102, 114, 138, 174, 186, 210, 222, 246, 258, 282, 318, 330, 354, 366, 390, 402, 426, 438, 462, 474, 498, 510, 534, 546, 570, 582, 606, 618, 642, 654, 678, 690, 714, 762, 770, 786, 798, 822, 834, 858, 870, 894, 906, 910, 930, 942, 966, 978 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

First odd term is 15015 = 3 * 5 * 7 * 11 * 13, with 32 divisors that add up to 32256 = 2*15015 + 2226. See A112643. - Alonso del Arte, Nov 06 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

A005117 INTERSECT A005101.

EXAMPLE

Checking that 30 = 2 * 3 * 5 and sigma(30) = 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 = 72, which is more than twice 30, we verify that 30 is in the sequence.

MAPLE

isA005101 := proc(n)

    simplify(numtheory[sigma](n)>2*n);

end proc:

isA087248 := proc(n)

    isA005101(n) and numtheory[issqrfree](n) ;

end proc:

for n from 1 to 500 do

    if isA087248(n) then

        print(n);

    end if;

end do: # R. J. Mathar, Nov 10 2014

MATHEMATICA

Select[Range[10^3], SquareFreeQ@ # && DivisorSigma[1, #] > 2 # &] (* Michael De Vlieger, Feb 05 2017 *)

PROG

(PARI) isA087248(i) = (sigma(i) > 2*i) && issquarefree(i) \\ Michel Marcus, Mar 09 2013

CROSSREFS

Cf. A087244-A087248, A008683, A005117, A005101, A112643.

Sequence in context: A034683 A328328 A302574 * A249242 A189759 A046401

Adjacent sequences:  A087245 A087246 A087247 * A087249 A087250 A087251

KEYWORD

nonn

AUTHOR

Labos Elemer, Sep 05 2003

STATUS

approved

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Last modified January 23 04:16 EST 2020. Contains 331168 sequences. (Running on oeis4.)