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

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