1,1

a(n) includes all terms of A023172(n) with terms 12*A072378(n) excluded. a(n) includes al1 powers of 5 = Fibonacci(5) and other numbers such as some multiples of Fibonacci(5^k). a(1) = Fibonacci(5) = 5, a(2)-a(6) = {5^2, 5^3, 5^4, 5^5, 5^6}, a(7) = 75025 = 5^2*3001 = Fibonacci(5^2), a(8) = 5^7, a(9) = 375125 = 5^3*3001 = 5*Fibonacci(5^2), a(10) = 5^8. Conjecture: a(n) includes all terms of geometric progressions of the form 5^k*Fibonacci(5m) for integers k>=0 and m>0. Open question: does a(n) include the powers of Fibonacci(5^k) and the terms of the form Fibonacci(5^k)*Fibonacci(5^m); or 1s it closed under multiplication?

Do[ If[ !IntegerQ[ n/12 ] && IntegerQ[ Fibonacci[n] / n ], Print[n] ], {n, 1, 5^8} ]

Cf. A072378 = numbers n such that 12n divides Fibonacci(12n). Cf. A023172 = numbers n such that n divides Fibonacci(n).

Sequence in context: A057831 A014946 A132839 this_sequence A102169 A060391 A000351

Adjacent sequences: A129063 A129064 A129065 this_sequence A129067 A129068 A129069

hard,more,nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), May 11 2007