A302972 a(n) is the smallest integer r such that A002828(r*n) = 4.

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

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 16 2018

Keywords

• nonn

Comments

All terms are squarefree.

Examples

			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.
		

Crossrefs

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

Programs

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)!=4, m++); m; } \\ Michel Marcus, Apr 17 2018

Formula

a(n^2) = 7.

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

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

Extensions

More terms from Michel Marcus, Apr 17 2018