A002659 - OEIS

%I M3762 N1536 #44 Nov 17 2017 04:03:29

%S 1,5,7,13,11,23,15,29,25,35,23,55,27,47,47,61,35,77,39,83,63,71,47,

%T 119,61,83,79,111,59,143,63,125,95,107,95,181,75,119,111,179,83,191,

%U 87,167,155,143,95,247,113,185,143,195,107,239,143,239,159,179,119,335,123,191

%N a(n) = 2*sigma(n) - 1.

%D 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 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Antti Karttunen, <a href="/A002659/b002659.txt">Table of n, a(n) for n = 1..16384</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F G.f. for Moebius transf.: (x + 2x^2 - x^3 ) / (1 - x )^2.

%F a(n) = A074400(n) - 1. - _Filip Zaludek_, Oct 30 2016

%t 2DivisorSigma[1,Range[70]]-1 (* _Harvey P. Dale_, Apr 14 2014 *)

%o (PARI) a(n)=if(n<1,0,2*sigma(n)-1)

%Y Cf. A000203, A002660, A002791, A074400.

%Y A row of the array in A242639.

%K easy,nonn

%O 1,2

%A _N. J. A. Sloane_, _Simon Plouffe_

%E Better definition from _Ralf Stephan_, Nov 18 2004