

A087156


Nonnegative numbers excluding 1.


13



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

1,2


COMMENTS

The old entry with this sequence number was a duplicate of A026835.
A063524(a(n)) = 0.  Reinhard Zumkeller, Oct 11 2008
Inverse binomial transform of A006589.  Philippe Deléham, Nov 25 2008
a(n) = maximum value of j, where 1 <= j <= n1, such that floor(j^2 / n) > 0 for each n.


LINKS

Table of n, a(n) for n=1..77.
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

G.f.: x^2*(2x)/(1x)^2 . E.g.f.: x*(exp(x)1).  Philippe Deléham, Nov 25 2008
a(n) = A163300(n)/2.  JuriStepan Gerasimov, Aug 14 2009
a(n) = n1+[(n+1) mod n], with n>=1.  Paolo P. Lava, Nov 06 2009
a(n) = n mod sigma_k(n), where sigma_k is the k divisor sigma function. Enrique Pérez Herrero, Nov 11 2009
a(n+1) = floor((n+sqrt(n^2+8n))/2).  Philippe Deléham, Oct 03 2011
a(n) = n mod n^2.  Andrew Secunda, Aug 21 2015


MATHEMATICA

A087156[n_] := Mod[n, DivisorSigma[1, n]] (* Enrique Pérez Herrero, Nov 11 2009 *)
Drop[Range[0, 80], {2}] (* Harvey P. Dale, Dec 13 2011 *)


PROG

(PARI) a(n)=n(n==1) \\ Charles R Greathouse IV, Aug 26 2011
(MAGMA) [n mod n^2: n in [1..100]]; // Vincenzo Librandi, Aug 22 2015


CROSSREFS

Cf. A000027, A166373.
Sequence in context: A303502 A000027 A001477 * A254109 A317945 A292579
Adjacent sequences: A087153 A087154 A087155 * A087157 A087158 A087159


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Oct 11 2008


EXTENSIONS

Comment and crossreference added by Christopher Hunt Gribble, Oct 14 2009, Oct 17 2009


STATUS

approved



