A302972 - OEIS

%I #9 May 03 2018 10:51:12

%S 7,14,5,7,3,10,1,14,7,6,5,5,3,2,1,7,7,14,5,3,3,10,1,10,7,6,5,1,3,2,1,

%T 14,7,14,5,7,3,10,1,6,7,6,5,5,3,2,1,5,7,14,5,3,3,10,1,2,7,6,5,1,3,2,1,

%U 7,7,14,5,7,3,10,1,14,7,6,5,5,3,2,1,3,7,14,5,3,3

%N a(n) is the smallest integer r such that A002828(r*n) = 4.

%C All terms are squarefree.

%F a(n^2) = 7.

%F a(n^2) + A302694(n^2) + A302690(n^2) + A007913(n^2) = 13.

%F a(n^2)*A302694(n^2)*A302690(n^2)*A007913(n^2) = 42.

%e a(1) = 7 because A002828(1*1) = 1, A002828(2*1) = 2, A002828(3*1) = 3, A002828(5*1) = 2, A002828(6*1) = 3, ..., and 7 is the smallest positive multiplier leading to A002828(7*1) = 7.

%o (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 isthree(n:int)=my(tmp=valuation(n, 2)); bitand(tmp, 1)||bitand(n>>tmp, 7)!=7;

%o a002828(n)=if(issquare(n), !!n, if(istwo(n), 2, 4-isthree(n))); \\ A002828

%o a(n) = {my(m=1); while(a002828(m*n)!=4, m++); m; } \\ _Michel Marcus_, Apr 17 2018

%Y Cf. A002828, A005117, A007913, A302690, A302694.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Apr 16 2018

%E More terms from _Michel Marcus_, Apr 17 2018