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%I #11 Apr 08 2022 09:01:55
%S 1,1,1,2,1,1,1,3,2,1,1,2,1,1,1,1,1,2,1,2,1,1,1,3,2,1,3,2,1,1,1,5,1,1,
%T 1,2,1,1,1,3,1,1,1,2,2,1,1,1,2,2,1,2,1,3,1,3,1,1,1,2,1,1,2,1,1,1,1,2,
%U 1,1,1,3,1,1,2,2,1,1,1,1,1,1,1,2,1,1,1,3,1,2,1,2,1,1,1,5,1,2,2,2
%N Maximal Fibonacci exponent in prime factorization of n, or 1 if there is no Fibonacci exponent.
%H Antti Karttunen, <a href="/A115568/b115568.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%t Module[{fibs=Fibonacci[Range[10]]},Table[Max[Select[FactorInteger[n][[All,2]],MemberQ[fibs,#]&]]/.(-\[Infinity]->1),{n,100}]] (* _Harvey P. Dale_, Apr 08 2022 *)
%o (PARI)
%o A010056(n) = { my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8)); } \\ This function from _Charles R Greathouse IV_, Jul 30 2012
%o A115568(n) = { my(exps=factorint(n)[, 2], expswith1 = vector(1+length(exps),i,if(1==i,i,exps[i-1]))); vecmax(apply(e -> (A010056(e)*e), expswith1)); }; \\ _Antti Karttunen_, Jul 23 2017
%Y Cf. A000045, A010056, A122895.
%K easy,nonn
%O 1,4
%A _Giovanni Teofilatto_, Mar 11 2006; revised Mar 13 2006
%E Corrected by _R. J. Mathar_, Apr 03 2012
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