OFFSET
1,1
COMMENTS
From Amiram Eldar, Sep 02 2022: (Start)
All the terms are even, since all the multiples of 6 that are larger than 6 are abundant numbers.
The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 8, 85, 865, 8716, 87668, 875528, 8761027, 87606693, 875947187, ... . Apparently, the asymptotic density of this sequence exists and equals 0.087... . (End)
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..10000
EXAMPLE
12 is abundant, 13, 14, 15, 16 and 17 are deficient, 18 is abundant.
24 is abundant, 25, 26, 27, 28 and 29 are deficient, 30 is abundant.
MAPLE
with(numtheory): A:=select(n->sigma(n)>2*n, [$1..800]): a:=seq(A[i], i in select(n->A[n+1]-A[n]=6, [$1..nops(A)-1]));
MATHEMATICA
q[n_] := DivisorSigma[1, n] > 2 n; Select[Range[600], q[#] && SelectFirst[# + Range[6], q] == # + 6 &] (* Giovanni Resta, Jul 01 2018 *)
PROG
(GAP) A:=Filtered([1..800], n->Sigma(n)>2*n);; a:=List(Filtered([1..Length(A)-1], i->A[i+1]-A[i]=6), j->A[j]);
CROSSREFS
KEYWORD
nonn
AUTHOR
Muniru A Asiru, Jun 25 2018
STATUS
approved