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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 (list; graph; refs; listen; history; text; internal format)
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 <= n-1, 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*(2-x)/(1-x)^2 . E.g.f.: x*(exp(x)-1). - Philippe Deléham, Nov 25 2008

a(n) = A163300(n)/2. - Juri-Stepan Gerasimov, Aug 14 2009

a(n) = n-1+[(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 A296086

Adjacent sequences:  A087153 A087154 A087155 * A087157 A087158 A087159

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Oct 11 2008

EXTENSIONS

Comment and cross-reference added by Christopher Hunt Gribble, Oct 14 2009, Oct 17 2009

STATUS

approved

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Last modified October 19 18:28 EDT 2018. Contains 316377 sequences. (Running on oeis4.)