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 A096399 Numbers k such that both k and k+1 are abundant. 34
 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 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. Set difference of sequences A103289 and {2^m-1} for m in A103291. 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. 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 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 June 6 18:03 EDT 2023. Contains 363149 sequences. (Running on oeis4.)