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%I #19 Jan 18 2019 01:24:08
%S 2,3,8,7,24,17,48,31,80,49,120,17,168,97,26,127,288,161,360,49,197,
%T 241,528,127,624,337,728,97,840,199,960,511,485,577,99,161,1368,721,
%U 170,351,1680,197,1848,241,649,1057,2208,127,2400,1249,577,337,2808,1457,1451
%N a(n) is the smallest value k > 1 such that k^2 - 1 is divisible by n^2.
%C a(n) = n^2 - 1 if n > 1 is in A235868. - _Robert Israel_, Jan 17 2019
%H Robert Israel, <a href="/A100836/b100836.txt">Table of n, a(n) for n = 1..10000</a> (first 500 terms from Harvey P. Dale)
%e a(4)=7 because 7^2 - 1 is divisible by 4^2 (and 7 is the smallest integer > 1 that satisfies this criterion).
%p f:= n -> min(map(t -> rhs(op(t)),{msolve(k^2-1,n^2)}) minus {1}):
%p f(1):= 2:
%p map(f, [$1..100]); # _Robert Israel_, Jan 17 2019
%t With[{c=Range[2,10000]},Flatten[Table[Select[c,Divisible[#^2-1, n^2]&, 1],{n,60}]]] (* _Harvey P. Dale_, Oct 23 2011 *)
%o (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 */
%Y Cf. A235868.
%K nonn,look
%O 1,1
%A Thomas Kerscher (Thomas.Kerscher(AT)web.de), Jan 19 2005
%E Entries confirmed by _Ray Chandler_, _R. J. Mathar_, and _Max Alekseyev_, Nov 21 2008
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