OFFSET
1,1
COMMENTS
Numbers k such that both sigma(k) > 2k and sigma(k+1) > 2*(k+1).
Numbers k such that both k and k+1 are in A005101.
The numbers of terms not exceeding 10^k, for k = 4, 5, ..., are 3, 27, 357, 3723, 36640, 365421, 3665799, 36646071, ... . Apparently, the asymptotic density of this sequence exists and equals 0.000366... . - Amiram Eldar, Sep 02 2022
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
Yong-Gao Chen, Hui Lv, On consecutive abundant numbers, arXiv:1603.06176 [math.NT], 2016.
Paul Erdős, Note on consecutive abundant numbers, J. London Math. Soc., 10 (1935), 128-131.
Carlos Rivera, Puzzle 878. Consecutive abundant integers, The Prime Puzzles and Problems Connection.
EXAMPLE
sigma(5775) = sigma(3*5*5*7*11) = 11904 > 2*5775.
sigma(5776) = sigma(2*2*2*2*19*19) = 11811 > 2*5776.
MATHEMATICA
fQ[n_] := DivisorSigma[1, n] > 2 n; Select[ Range@ 117000, fQ[ # ] && fQ[ # + 1] &] (* Robert G. Wilson v, Jun 11 2010 *)
Select[Partition[Select[Range[120000], DivisorSigma[1, #] > 2 # &], 2, 1], Differences@ # == {1} &][[All, 1]] (* Michael De Vlieger, May 20 2017 *)
PROG
(PARI) for(i=1, 1000000, if(sigma(i)>2*i && sigma(i+1)>2*(i+1), print(i))); \\ Max Alekseyev, Jan 28 2005
CROSSREFS
KEYWORD
nonn
AUTHOR
John L. Drost, Aug 06 2004
EXTENSIONS
Two further terms from Max Alekseyev, Jan 28 2005
Entry revised by N. J. A. Sloane, Dec 03 2006
Edited by T. D. Noe, Nov 15 2010
STATUS
approved