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A175454

a(n) = number of divisors of n(n+1) that divide neither n nor n+1.

0, 1, 2, 2, 3, 3, 3, 6, 6, 3, 5, 5, 3, 9, 12, 4, 5, 5, 5, 15, 9, 3, 7, 14, 6, 9, 15, 5, 7, 7, 5, 15, 9, 9, 24, 8, 3, 9, 21, 7, 7, 7, 5, 25, 15, 3, 9, 18, 10, 15, 15, 5, 7, 21, 21, 21, 9, 3, 11, 11, 3, 15, 30, 18, 21, 7, 5, 15, 21, 7, 11, 11, 3, 15, 25, 15, 21, 7, 9, 36, 12, 3, 11, 33, 9, 9, 21, 7 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,3`
	LINKS	`Antti Karttunen, Table of n, a(n) for n = 1..16385`
	FORMULA	`a(n) = (d(n)-1)*(d(n+1)-1), where d(n) = A000005(n).`
	PROG	`(PARI) A175454(n)={ local(a=0) ; fordiv(n(n+1), d, if(n %d <>0 && (n+1)%d<> 0, a++ ) ; ) ; return(a) ; }` `{ for(n=1, 120, print1(A175454(n)", ") ; ) ; } \\ R. J. Mathar, May 28 2010` `(PARI) A175454(n) = ((numdiv(n)-1)(numdiv(n+1)-1)); \\ Antti Karttunen, Oct 07 2017, after the given formula.`
	CROSSREFS	`Cf. A000005.` `Sequence in context: A293924 A307730 A169618 * A157501 A080968 A115733` `Adjacent sequences: A175451 A175452 A175453 * A175455 A175456 A175457`
	KEYWORD	`nonn`
	AUTHOR	`Leroy Quet, May 16 2010`
	EXTENSIONS	`More terms from Jon E. Schoenfield and R. J. Mathar, May 28 2010`
	STATUS	`approved`

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Last modified September 11 17:54 EDT 2024. Contains 375839 sequences. (Running on oeis4.)