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%I A002659 M3762 N1536 #44 Nov 17 2017 04:03:29
%S A002659 1,5,7,13,11,23,15,29,25,35,23,55,27,47,47,61,35,77,39,83,63,71,47,
%T A002659 119,61,83,79,111,59,143,63,125,95,107,95,181,75,119,111,179,83,191,
%U A002659 87,167,155,143,95,247,113,185,143,195,107,239,143,239,159,179,119,335,123,191
%N A002659 a(n) = 2*sigma(n) - 1.
%D A002659 P. A. MacMahon, The connexion between the sum of the squares of the divisors and the number of partitions of a given number, Messenger Math., 54 (1924), 113-116. Collected Papers, MIT Press, 1978, Vol. I, pp. 1364-1367.
%D A002659 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002659 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002659 Antti Karttunen, <a href="/A002659/b002659.txt">Table of n, a(n) for n = 1..16384</a>
%H A002659 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A002659 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A002659 G.f. for Moebius transf.: (x + 2x^2 - x^3 ) / (1 - x )^2.
%F A002659 a(n) = A074400(n) - 1. - _Filip Zaludek_, Oct 30 2016
%t A002659 2DivisorSigma[1,Range[70]]-1 (* _Harvey P. Dale_, Apr 14 2014 *)
%o A002659 (PARI) a(n)=if(n<1,0,2*sigma(n)-1)
%Y A002659 Cf. A000203, A002660, A002791, A074400.
%Y A002659 A row of the array in A242639.
%K A002659 easy,nonn
%O A002659 1,2
%A A002659 _N. J. A. Sloane_, _Simon Plouffe_
%E A002659 Better definition from _Ralf Stephan_, Nov 18 2004

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