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

Offset

1,1

Comments

All terms are squarefree.

Links

Table of n, a(n) for n=1..90.

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 A332552

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