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A096399 Numbers n such that both n and n+1 are abundant. 21
5775, 5984, 7424, 11024, 21735, 21944, 26144, 27404, 39375, 43064, 49664, 56924, 58695, 61424, 69615, 70784, 76544, 77175, 79695, 81080, 81675, 82004, 84524, 84644, 89775, 91664, 98175, 103455, 104895, 106784, 109395, 111824, 116655 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that both sigma(n)>2n and sigma(n+1)>2(n+1).

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, 128-131 (1935).

Carlos Rivera, Puzzle 878. Consecutive abundant integers

EXAMPLE

sigma(5775) = sigma(3*5*5*7*11) = 11904 > 2*5775.

sigma(5776) = sigma(2*2*2*2*19*19) = 11811 > 2*5776.

MAPLE

with(numtheory): P:=proc(n); if sigma(n)>2*n and sigma(n+1)>2*(n+1) then n;

fi; end: seq(P(i), i=1..10^6); # Paolo P. Lava, Jan 08 2018

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

Numbers n such that both n and n+1 are in A005105. Set difference of sequences A103289 and {2^m-1} for m in A103291.

Cf. A005101, A103289, A103291, A023196.

Sequence in context: A317049 A329525 A331202 * A071132 A228466 A094063

Adjacent sequences:  A096396 A096397 A096398 * A096400 A096401 A096402

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

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Last modified April 8 14:03 EDT 2020. Contains 333314 sequences. (Running on oeis4.)