A206096
Fibonacci numbers with 4 distinct prime divisors, each of multiplicity 1.
Original entry on oeis.org
6765, 196418, 317811, 2178309, 32951280099, 139583862445, 1304969544928657, 5527939700884757, 259695496911122585, 679891637638612258, 12200160415121876738, 83621143489848422977, 483162952612010163284885, 22698374052006863956975682
Offset: 1
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filter:= proc(t)
local F;
F:= ifactors(t)[2];
map(f -> f[2],F) = [1,1,1,1];
end proc:
select(filter, [seq(combinat:-fibonacci(n),n=1..200)]); # Robert Israel, Sep 07 2014
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Select[Fibonacci[Range[200]],Last/@FactorInteger[#]=={1,1,1,1}&]
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Vec(select(k -> omega(k)==4 && bigomega(k)==4, vector(100, i, fibonacci(i)))) \\ Edward Jiang, Sep 11 2014
A137574
Fibonacci numbers and their distinct prime divisors having the same number of decimal digits.
Original entry on oeis.org
2, 3, 5, 8, 13, 21, 89, 233, 1597, 17711, 28657, 46368, 75025, 121393, 514229, 1346269, 165580141, 433494437, 2971215073, 53316291173, 139583862445, 2504730781961, 308061521170129, 806515533049393, 14472334024676221, 99194853094755497, 19740274219868223167
Offset: 1
The Fibonacci number 53316291173 and its prime divisors 953 and 55945741 have exactly the same number of decimal digits.
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Select[Fibonacci[Range[3,100]],IntegerLength[#]==Total[IntegerLength/@First/@FactorInteger[#]]&] (* James C. McMahon, May 30 2025 *)
A206097
Fibonacci numbers F that are squarefree semiprimes such that F+2 or F-2 is also a squarefree semiprime.
Original entry on oeis.org
55, 4181, 17711, 121393, 5702887
Offset: 1
55 = Fibonacci(10) is a term because 55 = 5 * 11 and 55 + 2 = 57 = 3 * 19 are both squarefree semiprimes.
4181 = Fibonacci(19) is a term because 4181 = 37 * 113 and 4181 + 2 = 4183 = 47 * 89 are both squarefree semiprimes.
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Select[Fibonacci[Range[300]], Last/@FactorInteger[#]=={1,1} && (Last/@FactorInteger[#+2]=={1,1} || Last/@FactorInteger[#-2]=={1,1})&]
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