%I #10 Feb 06 2019 17:18:58
%S 2,4,2,10,2,3,2,6,2,4,2,3,2,4,2,12,2,3,2,5,2,4,2,3,2,4,2,7,2,3,2,6,2,
%T 4,2,3,2,4,2,5,2,3,2,6,2,4,2,3,2,4,2,12,2,3,2,6,2,4,2,3,2,4,2,10,2,3,
%U 2,6,2,4,2,3,2,4,2,12,2,3,2,5,2,4,2,3,2,4,2,11,2,3,2,6,2,4,2,3,2,4,2,5,2,3
%N Smallest k > 1 dividing tau(k*2^n) (cf. A000005).
%C Sequence contains the values 2,3,4,5,6,7,10,11,12 only. Is there any pattern ? a(m) = 4 for m =1,9,13,21,25,33,37,45,49,...This subsequence has the recurrence b(1)=1, b(2k)=b(2k-1)+8, b(2k+1)=b(2k)+4. If a(m) = 10 then m == 0 (mod 3). If m>n, a(n)=10, a(m)=10 then m-n == 0 (mod 60).
%H Antti Karttunen, <a href="/A072866/b072866.txt">Table of n, a(n) for n = 0..16384</a>
%o (PARI) A072866(n) = { n = (1<<n); for(k=2,oo,if(!(numdiv(k*n)%k), return(k))); }; \\ _Antti Karttunen_, Feb 06 2019
%Y Cf. A000005.
%K easy,nonn
%O 0,1
%A _Benoit Cloitre_, Jul 27 2002