A153193 a(n) is the number of integers of the form n*(n+1)*k / (k - n*(n+1)) where k is an integer >= 1.

4, 13, 22, 22, 40, 40, 31, 52, 67, 40, 67, 67, 40, 121, 121, 40, 67, 67, 67, 202, 121, 40, 94, 157, 67, 94, 157, 67, 121, 121, 49, 148, 121, 121, 337, 112, 40, 121, 283, 94, 121, 121, 67, 337, 202, 40, 121, 202, 112, 202, 202, 67, 94, 283, 283, 283, 121, 40

Offset

1,1

Comments

1/n - 1/(n+1) - 1/k = 1/c where c is an integer, k >= 1.

Links

Table of n, a(n) for n=1..58.

Example

The a(1)=4 integers of the form n*(n+1)*k/(k - n*(n+1)) = 1*(1+1)*k/(k - 1*(1+1)) = 2*k/(k-2) occur at
  k=1: 2*1/(1-2) = -2,
  k=3: 2*3/(3-2) =  6,
  k=4: 2*4/(4-2) =  4, and
  k=6: 2*6/(6-2) =  3.

Crossrefs

Cf. A146564, A152492, A063647, A000005, A146566.

Sequence in context: A063219 A063121 A199798 * A304905 A043469 A067396

Adjacent sequences: A153190 A153191 A153192 * A153194 A153195 A153196

Keyword

nonn

Author

Ctibor O. Zizka, Dec 20 2008

Extensions

a(13)-a(58) from Jon E. Schoenfield, Mar 15 2022

Status

approved