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A096399
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Numbers n such that both n and n+1 are abundant.
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21
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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
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OFFSET
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1,1
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COMMENTS
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Numbers n such that both sigma(n)>2n and sigma(n+1)>2(n+1).
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LINKS
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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
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EXAMPLE
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sigma(5775) = sigma(3*5*5*7*11) = 11904 > 2*5775.
sigma(5776) = sigma(2*2*2*2*19*19) = 11811 > 2*5776.
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) for(i=1, 1000000, if(sigma(i)>2*i && sigma(i+1)>2*(i+1), print(i))); \\ Max Alekseyev, Jan 28 2005
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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John L. Drost, Aug 06 2004
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EXTENSIONS
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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
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STATUS
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approved
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