cp's OEIS Frontend

A278245 Least number with the same prime signature as the n-th Fibonacci number: a(n) = A046523(A000045(n)).

%I A278245 #37 May 19 2017 06:02:53
%S A278245 1,1,2,2,2,8,2,6,6,6,2,144,2,6,30,30,2,120,6,210,30,6,2,10080,12,6,
%T A278245 210,210,2,9240,6,210,30,6,30,166320,30,30,30,30030,6,9240,2,2310,
%U A278245 2310,30,2,2882880,30,4620,30,210,6,120120,210,60060,2310,30,6,232792560,6,30,2310,30030,30,9240,30,2310,2310,510510,6,1396755360,6,210,4620,2310,210,120120,6
%N A278245 Least number with the same prime signature as the n-th Fibonacci number: a(n) = A046523(A000045(n)).
%C A278245 This sequence can be used as a filter for certain sequences involving Fibonacci numbers as it matches to any sequence that is obtained as f(A000045(n)), where f(n) is any function that depends only on the prime signature of n (see the index entry for "sequences computed from exponents in ...").
%C A278245 Matching in this context means that the sequence a matches with the sequence b iff for all i, j: a(i) = a(j) => b(i) = b(j). In other words, iff the sequence b partitions the natural numbers to the same or coarser equivalence classes (as/than the sequence a) by the distinct values it obtains.
%H A278245 Antti Karttunen (terms 1..374) & Hans Havermann, <a href="/A278245/b278245.txt">Table of n, a(n) for n = 1..1300</a>
%H A278245 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A278245 a(n) = A046523(A000045(n)).
%e A278245 From _Michael De Vlieger_, May 18 2017: (Start)
%e A278245 a(6) = 8 because Fibonacci(6) = 8, the multiplicity of the prime factor of 8 is 3; the smallest p^3 = 2^3 = 8.
%e A278245 a(7) = 2 because Fibonacci(7) = 13, the multiplicity of the prime factor of 13 is 1; the smallest p^1 = 2^1 = 2.
%e A278245 a(15) = 30 because Fibonacci(15) = 610. The multiplicities of the prime factors of 610, in order from greatest to least, are {1, 1, 1}, the smallest prime power product p^1 * q^1 * r^1 = 2 * 3 * 5 = 30.
%e A278245 a(18) = 120 because Fibonacci(18) = 2584 = 2^3 * 17 * 19 -> 2^3 * 3 * 5 = 120. (End)
%t A278245 Table[If[# == 1, 1, Times @@ MapIndexed[Prime[First[#2]]^#1 &,
%t A278245 Sort[FactorInteger[#][[All, -1]], Greater]]] &@ Fibonacci@ n, {n, 79}] (* _Michael De Vlieger_, May 18 2017 *)
%o A278245 (PARI)
%o A278245 A046523(n) = my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]) \\ From _Charles R Greathouse IV_, Aug 17 2011
%o A278245 f0 = 0; f1 = 1; for(n=1, 10000, write("b278245.txt", n, " ", A046523(f1)); old_f0 = f0; f0 = f1; f1 = f1 + old_f0; );
%o A278245 (Scheme) (define (A278245 n) (A046523 (A000045 n)))
%Y A278245 Cf. A000045, A046523, A278241, A278248.
%Y A278245 Cf. A286545 (rgs-version of this sequence), A286467.
%Y A278245 Cf. A001605 (positions of 2's), A072381 (of 6's).
%Y A278245 Sequences with matching equivalence classes: A063375, A105307, A152774.
%K A278245 nonn
%O A278245 1,3
%A A278245 _Antti Karttunen_, Nov 16 2016