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A087248
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Squarefree abundant numbers.
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12
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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
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1,1
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COMMENTS
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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
The asymptotic density of this sequence is larger than 0.0544 (Wall, 1970). - Amiram Eldar, Apr 18 2024
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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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;
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MATHEMATICA
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Select[Range[10^3], SquareFreeQ@ # && DivisorSigma[1, #] > 2 # &] (* Michael De Vlieger, Feb 05 2017 *)
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PROG
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(PARI) isA087248(i) = (sigma(i) > 2*i) && issquarefree(i) \\ Michel Marcus, Mar 09 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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