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A087156 Nonnegative numbers excluding 1. 13

%I

%S 0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,

%T 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,

%U 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77

%N Nonnegative numbers excluding 1.

%C The old entry with this sequence number was a duplicate of A026835.

%C A063524(a(n)) = 0. - _Reinhard Zumkeller_, Oct 11 2008

%C Inverse binomial transform of A006589. - _Philippe Deléham_, Nov 25 2008

%C a(n) = maximum value of j, where 1 <= j <= n-1, such that floor(j^2 / n) > 0 for each n.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: x^2*(2-x)/(1-x)^2 . E.g.f.: x*(exp(x)-1). - _Philippe Deléham_, Nov 25 2008

%F a(n) = A163300(n)/2. - _Juri-Stepan Gerasimov_, Aug 14 2009

%F a(n) = n-1+[(n+1) mod n], with n>=1. - _Paolo P. Lava_, Nov 06 2009

%F a(n) = n mod sigma_k(n), where sigma_k is the k divisor sigma function. -_Enrique Pérez Herrero_, Nov 11 2009

%F a(n+1) = floor((n+sqrt(n^2+8n))/2). - _Philippe Deléham_, Oct 03 2011

%F a(n) = n mod n^2. - _Andrew Secunda_, Aug 21 2015

%t A087156[n_] := Mod[n, DivisorSigma[1, n]] (* _Enrique Pérez Herrero_, Nov 11 2009 *)

%t Drop[Range[0,80],{2}] (* _Harvey P. Dale_, Dec 13 2011 *)

%o (PARI) a(n)=n-(n==1) \\ _Charles R Greathouse IV_, Aug 26 2011

%o (MAGMA) [n mod n^2: n in [1..100]]; // _Vincenzo Librandi_, Aug 22 2015

%Y Cf. A000027, A166373.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Oct 11 2008

%E Comment and cross-reference added by _Christopher Hunt Gribble_, Oct 14 2009, Oct 17 2009

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Last modified October 20 20:24 EDT 2019. Contains 328273 sequences. (Running on oeis4.)