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 A152012 Indices of Fibonacci numbers having exactly one primitive prime factor. 6
 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 43, 45, 47, 48, 51, 52, 54, 56, 60, 62, 63, 65, 66, 72, 74, 75, 76, 82, 83, 93, 94, 98, 105, 106, 108, 111, 112, 119, 121, 122, 123, 124, 125, 131 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It is known that Fibonacci number A000045(n) has a primitive prime factor for all n, except n=0, 1, 2, 6 and 12. This sequence lists such indices n that A000045(n) has exactly one primitive prime factor (equal A001578(n)). Sister sequence A152013 provides indices of Fibonacci numbers with at least 2 prime factors. The current sequence A152012 and its sister sequence A152013 along with the finite set {0,1,2,6,12} form a partition of the natural numbers. Numbers n such that A086597(n) = 1. For prime p, all prime factors of Fibonacci(p) are primitive. Hence, the only primes in this sequence are the primes numbers in A001605, which gives the indices of prime Fibonacci numbers. LINKS T. D. Noe, Table of n, a(n) for n=1..392 MATHEMATICA primitivePrimeFactors[n_] := Cases[FactorInteger[Fibonacci[n]][[All, 1]], p_ /; And @@ (GCD[p, #] == 1 & /@ Array[Fibonacci, n-1])]; Reap[For[n=3, n <= 200, n++, If[Length[primitivePrimeFactors[n]] == 1, Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Dec 12 2014 *) PROG (PARI) isok(pf, vp) = sum(i=1, #pf, vecsearch(vp, pf[i]) == 0) == 1; lista(nn) = {vp = []; for (n=3, nn, pf = factor(fibonacci(n))[, 1]; if (isok(pf, vp), print1(n, ", ")); vp = vecsort(concat(vp, pf), , 8); ); } \\ Michel Marcus, Nov 29 2014 CROSSREFS Cf. A000045, A001578, A152013. Sequence in context: A184431 A078358 A175968 * A173153 A231711 A039131 Adjacent sequences:  A152009 A152010 A152011 * A152013 A152014 A152015 KEYWORD nonn AUTHOR Max Alekseyev, Nov 19 2008 STATUS approved

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Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)