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A302690 a(n) is the smallest integer m such that A002828(m*n) = 2. 3
2, 1, 6, 2, 1, 3, 14, 1, 2, 1, 22, 6, 1, 7, 3, 2, 1, 1, 38, 1, 42, 11, 46, 3, 2, 1, 6, 14, 1, 3, 62, 1, 66, 1, 7, 2, 1, 19, 3, 1, 1, 21, 86, 22, 1, 23, 94, 6, 2, 1, 3, 1, 1, 3, 11, 7, 114, 1, 118, 3, 1, 31, 14, 2, 1, 33, 134, 1, 138, 7, 142, 1, 1, 1, 6, 38, 154, 3, 158 (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..79.

FORMULA

a(n^2) = 2.

EXAMPLE

a(3) = 6 because A002828(1*3) = 3, A002828(2*3) = 3, A002828(3*3) = 1, A002828(5*3) = 4, ..., and 6 is the smallest positive multiplier leading to A002828(6*3) = 2.

MAPLE

A302690 := proc(n)

    local k ;

    for k from 1 do

        if A002828(k*n) = 2 then

            return k;

        end if;

    end do:

end proc:

seq(A302690(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)!=2, m++); m; } \\ Michel Marcus, Apr 12 2018

CROSSREFS

Cf. A002828, A005117, A007913, A064680, A099304, A302694.

Sequence in context: A083720 A055878 A331654 * A030304 A248779 A286030

Adjacent sequences:  A302687 A302688 A302689 * A302691 A302692 A302693

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 August 10 11:12 EDT 2020. Contains 336379 sequences. (Running on oeis4.)