A087156 Nonnegative numbers excluding 1.

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

Offset: 1

Author

N. J. A. Sloane, Oct 11 2008

Keywords

• nonn
• easy

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

• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A000027, A166373.

Programs

Magma

[n mod n^2: n in [1..100]]; // Vincenzo Librandi, Aug 22 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 *)

PARI

a(n)=n-(n==1) \\ Charles R Greathouse IV, Aug 26 2011

Python

def A087156(n): return n if n>1 else 0 # Chai Wah Wu, Jul 31 2024

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 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

Extensions

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