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A089655 a(1)=1 and for n>=2 a(n) is the denominator of A(n) (see comment for A(n) definition). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A196757 A193254 A193454 * A097936 A277027 A050338

Adjacent sequences:  A089652 A089653 A089654 * A089656 A089657 A089658

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jan 03 2004

STATUS

approved

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Last modified December 7 23:05 EST 2016. Contains 278900 sequences.