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A302694 a(n) is the smallest integer k such that A002828(k*n) = 3.

%I A302694 #30 Apr 16 2018 11:29:45
%S A302694 3,3,1,3,6,1,2,3,3,3,1,1,6,1,2,3,3,3,1,6,1,1,2,1,3,3,1,2,6,1,2,3,1,3,
%T A302694 1,3,6,1,2,3,3,1,1,1,6,1,2,1,3,3,1,6,6,1,2,1,1,3,1,2,6,1,2,3,3,1,1,3,
%U A302694 1,1,2,3,3,3,1,1,1,1,2,6,3,3,1,1,6,1,2,1,3,3
%N A302694 a(n) is the smallest integer k such that A002828(k*n) = 3.
%C A302694 All terms are squarefree.
%F A302694 a(n^2) = 3.
%F A302694 Conjecture: a(n) <= 6.
%e A302694 a(2) = 3 because A002828(1*2) = 2, A002828(2*2) = 1,..., and 3 is the smallest multiplier leading to A002828(3*2) = 3.
%p A302694 A302694 := proc(n)
%p A302694     for k from 1 do
%p A302694         if A002828(k*n) = 3 then
%p A302694             return k;
%p A302694         end if;
%p A302694     end do:
%p A302694 end proc:
%p A302694 seq(A302694(n),n=1..100) ; # _R. J. Mathar_, Apr 16 2018
%o A302694 (PARI) istwo(n:int)=my(f); if(n<3, return(n>=0); ); f=factor(n>>valuation(n, 2)); for(i=1, #f[, 1], if(bitand(f[i, 2], 1)==1&&bitand(f[i, 1], 3)==3, return(0))); 1;
%o A302694 isthree(n:int)=my(tmp=valuation(n, 2)); bitand(tmp, 1)||bitand(n>>tmp, 7)!=7;
%o A302694 a002828(n)=if(issquare(n), !!n, if(istwo(n), 2, 4-isthree(n))); \\ A002828
%o A302694 a(n) = {my(m=1); while(a002828(m*n)!=3, m++); m; } \\ _Michel Marcus_, Apr 12 2018
%Y A302694 Cf. A002828, A005117, A007521, A007913, A302690.
%K A302694 nonn
%O A302694 1,1
%A A302694 _Juri-Stepan Gerasimov_, Apr 11 2018
%E A302694 Name corrected and more terms added by _Michel Marcus_, Apr 12 2018