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 A302694 a(n) is the smallest integer k such that A002828(k*n) = 3. 3
 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, 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, 1, 1, 2, 3, 3, 3, 1, 1, 1, 1, 2, 6, 3, 3, 1, 1, 6, 1, 2, 1, 3, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All terms are squarefree. LINKS FORMULA a(n^2) = 3. Conjecture: a(n) <= 6. EXAMPLE a(2) = 3 because A002828(1*2) = 2, A002828(2*2) = 1,..., and 3 is the smallest multiplier leading to A002828(3*2) = 3. MAPLE A302694 := proc(n)     for k from 1 do         if A002828(k*n) = 3 then             return k;         end if;     end do: end proc: seq(A302694(n), n=1..100) ; # R. J. Mathar, Apr 16 2018 PROG (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; isthree(n:int)=my(tmp=valuation(n, 2)); bitand(tmp, 1)||bitand(n>>tmp, 7)!=7; a002828(n)=if(issquare(n), !!n, if(istwo(n), 2, 4-isthree(n))); \\ A002828 a(n) = {my(m=1); while(a002828(m*n)!=3, m++); m; } \\ Michel Marcus, Apr 12 2018 CROSSREFS Cf. A002828, A005117, A007521, A007913, A302690. Sequence in context: A317931 A002332 A332547 * A245668 A002102 A209334 Adjacent sequences:  A302691 A302692 A302693 * A302695 A302696 A302697 KEYWORD nonn AUTHOR Juri-Stepan Gerasimov, Apr 11 2018 EXTENSIONS Name corrected and more terms added by Michel Marcus, Apr 12 2018 STATUS approved

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Last modified February 23 12:38 EST 2020. Contains 332159 sequences. (Running on oeis4.)