A089655 - OEIS

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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).

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: A193254 A193454 A322819 * A322820 A097936 A277027` `Adjacent sequences: A089652 A089653 A089654 * A089656 A089657 A089658`
	KEYWORD	`nonn`
	AUTHOR	`Benoit Cloitre, Jan 03 2004`
	STATUS	`approved`

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Last modified April 2 01:40 EDT 2023. Contains 361723 sequences. (Running on oeis4.)