OFFSET
1,1
COMMENTS
The first odd term is <= 76728582876430878992529528245373 (see A294025). Note that there are infinitely many odd terms, since if k is an odd term then 2*t*k*(k+2) + k are odd terms for all t >= 0. - Jianing Song, Nov 13 2022
From Amiram Eldar, May 30 2023: (Start)
The least odd term is larger than 10^11.
The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 7, 81, 820, 8074, 80410, 804623, 8040362, 80414534, 804257458, 8042148484, ... . Apparently, the asymptotic density of this sequence exists and equals 0.08042... . (End)
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Shyam Sunder Gupta)
EXAMPLE
18, 20 are abundant, thus the smaller number is listed.
MAPLE
withnumtheory: select(n->sigma(n)>2*n and sigma(n+1)<2*(n+1) and sigma(n+2)>2*(n+2), [$1..700]); # Muniru A Asiru, Jun 24 2018
MATHEMATICA
AbundantQ[n_] := DivisorSigma[1, n] > 2n; m = 0; a2 = {}; Do[If[AbundantQ[n], m = m + 1; If[m > 1, AppendTo[a2, n - 2]], m = 0], {n, 2, 100000, 2}]; a2
Module[{nn=650, sa}, sa=Table[If[DivisorSigma[1, n]>2n, 1, 0], {n, nn}]; Transpose[ SequencePosition[sa, {1, 0, 1}]]][[1]] (* The program uses the SequencePosition function from Mathematica version 10 *) (* Harvey P. Dale, May 20 2016 *)
PROG
(PARI) is(n)=sigma(n, -1)>2 && sigma(n+2, -1)>2 \\ Charles R Greathouse IV, Feb 21 2017
(GAP) A:=Filtered([1..700], n->Sigma(n)>2*n);; a:=List(Filtered([1..Length(A)-1], i->A[i+1]=A[i]+2), j->A[j]); # Muniru A Asiru, Jun 24 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Shyam Sunder Gupta, Nov 03 2013
STATUS
approved