

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
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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
The lower asymptotic density of this sequence is larger than 1/(2*Pi^2) = 0.05066... which is the density of its subsequence of squarefree numbers larger than 6 and divisible by 6. The number of terms below 10^k for k=1,2,... is 0, 5, 53, 556, 5505, 55345, 551577, 5521257, 55233676, 552179958, 5521420147, ..., so it seems that this sequence has an asymptotic density which equals to about 0.05521...  Amiram Eldar, Feb 13 2021


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. A087244A087248, 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



