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 A130164 Numbers k such that k^2 divides 3*Fibonacci(k). 2
 1, 12, 36, 612, 684, 3852, 11628, 25308, 41004, 65484, 73188, 77292, 155268, 156636, 250308, 430236, 467172, 545148, 562428, 779076, 977364, 1244196, 1313964, 1847484, 2123028, 2185452, 2621196, 2639556, 2662812, 2707956, 2859804, 3770892, 4387428, 4679244, 4755852, 4942116, 5744916, 5795532, 6394716, 7941924, 8053308, 8270244, 9267516 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A subset of A023172. All listed terms for n>1 are divisible by a(2) = 12 = 2^2*3. All listed terms for n>2 are divisible by a(3) = 36 = 2^2*3^2. - Robert G. Wilson v, May 15 2007 LINKS Giovanni Resta, Table of n, a(n) for n = 1..289 (terms < 4*10^9) EXAMPLE 36 is a term because 36^2 = 2^4*3^4 divides 3*Fibonacci(36) = 3*14930352 = 2^4*3^4*17*19*107. MATHEMATICA a=0; b=1; c=1; Do[ a=b; b=c; c=a+b; If[ Mod[3c, (n+2)^2 ] == 0, Print[n+2]], {n, 1, 30000}] (* Stefan Steinerberger, May 15 2007 *) a = 0; b = 0; c = 1; lst = {}; Do[ If[ Mod[3c, n^2] == 0, AppendTo[lst, n]]; a = b; b = c; c = a + b; {n, 2000000}]; lst (* Robert G. Wilson v *) A130164 = {1}; a = 0; b = 12; c = 3864; Do[If[Mod[36b, n^2] == 0, A130164 = Append[A130164, n]]; a = b; b = c; c = 322b - a; , {n, 12, 1000000, 12}]; A130164 Length[A130164] (* Keith Schneider, May 27 2007 *) PROG (PARI) for(n=1, 10^7, A=matrix(2, 2, i, j, Mod(1, n*n)*(i+j<4))^n; if(lift(3*A[1, 2])==0, print1(n", "))) (Magma) [n: n in [1..2*10^5] | 3*Fibonacci(n) mod n^2 eq 0 ]; // Vincenzo Librandi, Sep 17 2015 CROSSREFS Cf. A000045. Cf. A023172 (n divides Fibonacci(n)), A130163 (n^2 divides 2*Fibonacci(n)). Sequence in context: A085331 A225100 A058040 * A144973 A043358 A023731 Adjacent sequences: A130161 A130162 A130163 * A130165 A130166 A130167 KEYWORD nonn AUTHOR Alexander Adamchuk, May 14 2007 EXTENSIONS More terms from Stefan Steinerberger and Robert G. Wilson v, May 15 2007 More terms from Robert Gerbicz, Nov 28 2010 STATUS approved

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Last modified July 22 12:22 EDT 2024. Contains 374499 sequences. (Running on oeis4.)