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 A100836 a(n) is the smallest value k > 1 such that k^2 - 1 is divisible by n^2. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = n^2 - 1 if n > 1 is in A235868. - Robert Israel, Jan 17 2019 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 (first 500 terms from Harvey P. Dale) EXAMPLE a(4)=7 because 7^2 - 1 is divisible by 4^2 (and 7 is the smallest integer > 1 that satisfies this criterion). 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 *) PROG (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 */ CROSSREFS Cf. A235868. Sequence in context: A171046 A250116 A318949 * A173162 A198104 A237643 Adjacent sequences:  A100833 A100834 A100835 * A100837 A100838 A100839 KEYWORD nonn,look AUTHOR Thomas Kerscher (Thomas.Kerscher(AT)web.de), Jan 19 2005 EXTENSIONS Entries confirmed by Ray Chandler, R. J. Mathar, and Max Alekseyev, Nov 21 2008 STATUS approved

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Last modified January 19 06:28 EST 2021. Contains 340266 sequences. (Running on oeis4.)