A292430 Record numbers of unordered triples {a, b, c} of distinct positive integers from 1 to n such that a*b = c*n.

0, 2, 4, 8, 13, 16, 26, 38, 46, 50, 56, 71, 74, 120, 136, 176, 193, 214, 330, 355, 482, 574, 668, 839, 890, 996, 1088, 1223, 1528, 1920, 2039, 2224, 2374, 2646, 3055, 3120, 3811, 5010, 5539, 6208, 6591, 8566, 9139, 9690, 12359, 13894, 14796, 15331, 16118, 16558

Offset

1,2

Comments

Record numbers of ordered triples {a, b, c} of positive integers such that a*b = c*n with c < a < b < n.

Links

Table of n, a(n) for n=1..50.

Formula

a(n) = A278648(A292431(n)).

Example

There are 4 unordered triples {a, b, c} of distinct positive integers from 1 to 10 such that a*b = c*10:
  {2, 5, 1}: 2*5 = 1*10 = 10;
  {4, 5, 2}: 4*5 = 2*10 = 20;
  {5, 6, 3}: 5*6 = 3*10 = 30;
  {5, 8, 4}: 5*8 = 4*10 = 40.
This is more than any n < 10, so 4 is in this sequence.

Crossrefs

Records in A278648.

Cf. A292431.

Sequence in context: A107326 A018671 A018442 * A018335 A030058 A346992

Adjacent sequences: A292427 A292428 A292429 * A292431 A292432 A292433

Keyword

nonn

Author

Bobby Jacobs and Robert G. Wilson v, Sep 30 2017

Status

approved