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

1,3

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.

Links

Table of n, a(n) for n=1..94.

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

Crossrefs

Cf. A007947.

Sequence in context: A193454 A368921 A322819 * A322820 A097936 A277027

Adjacent sequences: A089652 A089653 A089654 * A089656 A089657 A089658

Keyword

nonn

Author

Benoit Cloitre, Jan 03 2004

Status

approved