A066451 a(n) is the number of integers k > 0 such that (n*k+1)/(k^2+1) is an integer.

1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 2, 3, 1, 2, 1, 3, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 1, 2, 1, 3, 2, 3, 1, 2, 1, 3, 2, 2, 1, 2, 2, 4, 1, 2, 1, 3, 1, 2, 1, 2, 2, 3, 1, 3, 1, 5, 1, 2, 1, 2, 2, 3, 1, 2, 1, 3, 1, 2, 1, 2, 3, 4, 1, 2, 1, 3, 1, 2, 2, 2, 2, 4, 1, 2, 1, 3, 1, 3, 1, 3, 2, 3, 1, 2, 1, 3, 1, 2, 1, 2, 2, 3, 1, 2

Offset

1,3

Links

Table of n, a(n) for n=1..105.

Example

a(57)=5 because (57*k+1)/(k^2+1) is an integer for k = 1,2,5,7,57.

Prog

(PARI) a(n) = sum(k=1, n, denominator((n*k+1)/(k^2+1)) == 1); \\ Michel Marcus, Feb 17 2021

Crossrefs

Sequence in context: A195155 A178544 A161506 * A328048 A363522 A091090

Adjacent sequences: A066448 A066449 A066450 * A066452 A066453 A066454

Keyword

nonn

Author

Benoit Cloitre, Dec 29 2001

Status

approved