%I A059957
%S A059957 1,2,2,2,3,3,2,2,3,3,3,3,3,4,3,2,3,3,3,4,4,3,3,3,3,3,3,3,4,4,2,3,4,4,4,
%T A059957 3,3,4,4,3,4,4,3,4,4,3,3,3,3,4,4,3,3,4,4,4,4,3,4,4,3,4,3,3,5,4,3,4,5,4,
%U A059957 3,3,3,4,4,4,5,4,3,3,3,3,4,5,4,4,4,3,4,5,4,4,4,4,4,3,3,4,4,3,4,4,3,5,5
%N A059957 Sum of distinct prime factors of n and n+1, or number of prime factors 
               of n(n+1) or of LCM[n,n+1].
%C A059957 If a(n)=2, then n is in A006549, being either a Mersenne prime, a Fermat 
               prime minus one, or n=8, corresponding to the unique solution to 
               Catalan's equation, 3^2 = 2^3 + 1. - Gene Ward Smith (genewardsmith(AT)gmail.com), 
               Sep 07 2006
%F A059957 a(n) = A001221(A002378(n)) = A001221(n*(n+1)) = A001221(n)+A001221(n+1) 
               because GCD[n, n+1] = 1.
%e A059957 If a(n)=2, then n is in A006549 (Mersenne-primes, Fermat-primes-1). n=30030, 
               n has 6 prime factors, 30001=59*509 so a(30030)=6+2=8 n=30029 a(30029)=1+6=7
%e A059957 n=30030, n has 6 prime factors, 30001=59*509 so a(30030)=6+2=8 n=30029 
               a(30029)=1+6=7
%Y A059957 Cf. A006549, A001221, A002378.
%Y A059957 Sequence in context: A124064 A096916 A098014 this_sequence A165924 A094528 
               A077774
%Y A059957 Adjacent sequences: A059954 A059955 A059956 this_sequence A059958 A059959 
               A059960
%K A059957 nonn
%O A059957 1,2
%A A059957 Labos E. (labos(AT)ana.sote.hu), Mar 02 2001