A174435 lambda(y)/x, where y an odd squarefree semiprime and x = ord(2,y) the smallest positive integer such that 2^x == 1 mod y (the multiplicative order of 2 mod y).

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 4, 2, 1, 1, 1, 1, 1, 1, 1, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 4, 3, 1, 2, 1, 1, 9, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 5, 1, 3, 3, 1, 2, 1, 2, 2, 1, 1, 8, 1, 1, 1, 6

Offset: 1

Author

Vassilis Papadimitriou, Mar 19 2010

Keywords

• nonn

Examples

			For n=1 the a(1)= 1, as the first odd squarefree semiprime is 15, lambda(15)=4 and ord(2,15)=4
		

Links

• Vassilis Papadimitriou, Table of n, a(n) for n=1,...,10000.

Crossrefs

Cf. A002322, A002326, A046388, A174240.

Programs

Mathematica

(CarmichaelLambda[#]/MultiplicativeOrder[2, #]) & /@ Select[Range[1, 530, 2], PrimeOmega[#] == 2 && PrimeNu[#] == 2 &] (* Amiram Eldar, Feb 24 2021 *)

Formula

Equals lambda(A046388)/ord(2, A046388), or lambda(A046388)/A174240.

a(n) = A002322(A046388(n))/A002326((A046388(n)+1)/2). - Amiram Eldar, Feb 24 2021