135721

Properties

Appears in sequences

• Smallest primitive prime factor of Fibonacci number F(n), or 1 if F(n) has no primitive prime factor.at n=38A001578
• a(n) = F(n) / Product_{p|n} F(p), where F(k) is k-th Fibonacci number and the p's in product are the distinct primes dividing n.at n=38A051348
• Values of C (the hypotenuse) of a Pythagorean triangle with A (the short leg) and C both prime and part of a twin prime.at n=7A051859
• Largest prime factor of n-th Fibonacci number.at n=36A060385
• Primitive part of Fibonacci(n).at n=38A061446
• Factorize the Fibonacci numbers in order, skipping F(0)-F(2), F(6)=8 and F(12)=144; at each step at least one new prime will occur; append to the sequence the smallest such new prime.at n=34A061488
• Numbers having exactly four anti-divisors.at n=34A066469
• Prime hypotenuses of Pythagorean triangles with a prime leg.at n=20A067756
• a(n+1) - 3*a(n) + a(n-1) = (2/3)(1+w^(n+1)+w^(2n+2)), where w = exp(2 Pi I / 3).at n=13A071618
• Smallest prime of the form 1 followed by a perfect power.at n=31A089773
• Expansion of x*(1+3*x+2*x^2)/((1+x+x^2)*(1-x-x^2)).at n=25A100886
• Expansion of (1-x)*(2*x^2+2*x+1) / ((x^2-x-1)*(x^2+x+1)).at n=25A111734
• a(n) = F(n)/Product_{p=primes} F(p^(m_{n,p})), where p^(m_{n,p}) is highest power of p dividing n, m= nonnegative integer and F(k) is the k-th Fibonacci number.at n=38A113196
• a(n) = F(n-th squarefree)/product{p=primes,p|(n-th squarefree)} F(p), where F(m) is m-th Fibonacci number.at n=25A115022
• a(n) = 3*a(n-1) + 5*a(n-2) + a(n-3).at n=8A120775
• Primes of the form 50n^2 + 10n + 1.at n=22A154428
• a(n) = floor(Lucas(n+1)/2), Lucas(n) = A000032(n).at n=25A173714
• Partial sums of odd Fibonacci numbers (A014437).at n=16A174542
• a(n) = numerator of Sum_{i=1..n} binomial(2n-i-1,i-1)/i.at n=12A175385
• Prime numbers that are Fibonacci integers.at n=38A178762