A089655 a(1)=1 and for n>=2 a(n) is the denominator of A(n) (see comment for A(n) definition).

1, 1, 4, 1, 4, 1, 8, 3, 8, 3, 4, 1, 4, 1, 16, 1, 48, 1, 12, 1, 4, 1, 8, 5, 8, 45, 4, 9, 4, 1, 32, 1, 32, 1, 12, 1, 12, 1, 8, 1, 8, 1, 4, 3, 4, 3, 16, 7, 80, 7, 20, 1, 36, 1, 72, 1, 8, 1, 4, 1, 4, 3, 64, 3, 64, 1, 4, 1, 4, 1, 24, 1, 24, 5, 4, 5, 4, 1, 16, 27, 16, 27, 4, 1, 4, 1, 8, 1, 24, 1, 12, 1, 4, 1

Offset: 1

Author

Benoit Cloitre, Jan 03 2004

Keywords

• nonn

Comments

For n>=2, A(n) is the least rational value >1 such that A(n)*(n^(2k)-1)*B(2k) is an integer value for k=1 up to 200, where B(2k) is the 2k-th Bernoulli number. It appears that sequence of numerators of A(n) coincide with A007947 (terms were computed by W. Edwin Clark). We conjecture : A(n)*(n^(2k)-1)*B(2k) is an integer value for all k>0.

Crossrefs

Cf. A007947.

Formula

It appears that if p is prime and 2^p-1 and (2^p+1)/3 are both primes (i.e. p is in A000043 and in A000978), then a(2^p)=(4^p-1)/3 (converse doesn't hold).

For n>1 a(n)=(n^2-1)/rad(n^2-1) where rad(k) is the squarefree kernel of k; a(n)=A003557(n^2-1) - Benoit Cloitre, Oct 26 2004