cp's OEIS Frontend

A087156 Nonnegative numbers excluding 1.

%I A087156 #47 Aug 01 2024 01:37:01
%S A087156 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 A087156 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U A087156 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 A087156 Nonnegative numbers excluding 1.
%C A087156 The old entry with this sequence number was a duplicate of A026835.
%C A087156 A063524(a(n)) = 0. - _Reinhard Zumkeller_, Oct 11 2008
%C A087156 Inverse binomial transform of A006589. - _Philippe Deléham_, Nov 25 2008
%C A087156 a(n) = maximum value of j, where 1 <= j <= n-1, such that floor(j^2 / n) > 0 for each n.
%H A087156 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A087156 G.f.: x^2*(2-x)/(1-x)^2 . E.g.f.: x*(exp(x)-1). - _Philippe Deléham_, Nov 25 2008
%F A087156 a(n) = A163300(n)/2. - _Juri-Stepan Gerasimov_, Aug 14 2009
%F A087156 a(n) = n mod sigma_k(n), where sigma_k is the k divisor sigma function. -_Enrique Pérez Herrero_, Nov 11 2009
%F A087156 a(n+1) = floor((n+sqrt(n^2+8n))/2). - _Philippe Deléham_, Oct 03 2011
%F A087156 a(n) = n mod n^2. - _Andrew Secunda_, Aug 21 2015
%t A087156 A087156[n_] := Mod[n, DivisorSigma[1, n]] (* _Enrique Pérez Herrero_, Nov 11 2009 *)
%t A087156 Drop[Range[0,80],{2}] (* _Harvey P. Dale_, Dec 13 2011 *)
%o A087156 (PARI) a(n)=n-(n==1) \\ _Charles R Greathouse IV_, Aug 26 2011
%o A087156 (Magma) [n mod n^2: n in [1..100]]; // _Vincenzo Librandi_, Aug 22 2015
%o A087156 (Python)
%o A087156 def A087156(n): return n if n>1 else 0 # _Chai Wah Wu_, Jul 31 2024
%Y A087156 Cf. A000027, A166373.
%K A087156 nonn,easy
%O A087156 1,2
%A A087156 _N. J. A. Sloane_, Oct 11 2008
%E A087156 Comment and cross-reference added by _Christopher Hunt Gribble_, Oct 14 2009, Oct 17 2009