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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

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 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 March 29 05:39 EDT 2020. Contains 333105 sequences. (Running on oeis4.)