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
The asymptotic density of this sequence is larger than 0.0544 (Wall, 1970). - Amiram Eldar, Apr 18 2024
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Charles Robert Wall, Topics related to the sum of unitary divisors of an integer, Ph.D. diss., University of Tennessee, 1970.
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Sep 05 2003
STATUS
approved