A100836 a(n) is the smallest value k > 1 such that k^2 - 1 is divisible by n^2.

2, 3, 8, 7, 24, 17, 48, 31, 80, 49, 120, 17, 168, 97, 26, 127, 288, 161, 360, 49, 197, 241, 528, 127, 624, 337, 728, 97, 840, 199, 960, 511, 485, 577, 99, 161, 1368, 721, 170, 351, 1680, 197, 1848, 241, 649, 1057, 2208, 127, 2400, 1249, 577, 337, 2808, 1457, 1451

Offset: 1

Author

Thomas Kerscher (Thomas.Kerscher(AT)web.de), Jan 19 2005

Keywords

• nonn
• look

Comments

a(n) = n^2 - 1 if n > 1 is in A235868. - Robert Israel, Jan 17 2019

Examples

			a(4)=7 because 7^2 - 1 is divisible by 4^2 (and 7 is the smallest integer > 1 that satisfies this criterion).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000 (first 500 terms from Harvey P. Dale)

Crossrefs

Cf. A235868.

Programs

Maple

f:= n -> min(map(t -> rhs(op(t)),{msolve(k^2-1,n^2)}) minus {1}):
f(1):= 2:
map(f, [$1..100]); # Robert Israel, Jan 17 2019

Mathematica

With[{c=Range[2,10000]},Flatten[Table[Select[c,Divisible[#^2-1, n^2]&, 1],{n,60}]]] (* Harvey P. Dale, Oct 23 2011 *)

PARI

{ A100836(n)=local(f,b,t,m); if(n==1,return(1)); if(n==2,return(3));t=valuation(n,2); if(n==2^t, return(2^(2*t-1)-1)); f=factorint(n/2^t);f=vector(matsize(f)[1],j,f[j,1]^(2*f[j,2])); if(t>0, f=concat(f,[2^(2*t-1)])); b=n^2+1; forvec(v=vector(#f,i,[0,1]), m=lift(chinese(vector(#f,j,Mod((-1)^v[j],f[j])))); if(m>1, b=min(b,m)); ); b } /* Max Alekseyev, Nov 21 2008 */

Extensions

Entries confirmed by Ray Chandler, R. J. Mathar, and Max Alekseyev, Nov 21 2008