A375499 a(n) is the smallest number of straight lines needed to intersect all points (k, d(k)) for k = 1..n (where d is the sum-of-divisors function A000005).

1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11

Offset

1,3

Links

Max Alekseyev, Table of n, a(n) for n = 1..400

Max Alekseyev, Sage program for lines covering points, Github, Aug 19 2024

Rémy Sigrist, PARI program

N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]

Example

The initial terms, together with an appropriate set of lines, are:
  1 1 [1]
  2 1 [x]
  3 2 [2, x]
  4 2 [2, (2/3)*x + 1/3]
  5 2 [2, (2/3)*x + 1/3]
  6 3 [2, 2*x - 8, (2/3)*x + 1/3]
  7 3 [2, 2*x - 8, (2/3)*x + 1/3]
  8 3 [2, 4, (2/3)*x + 1/3]
  9 4 [2, 3, 4, x]
  10 4 [2, 3, 4, x]
  11 4 [2, 3, 4, x]
  12 4 [2, 3, 4, (5/11)*x + 6/11]
  13 4 [2, 3, 4, (5/11)*x + 6/11]
  14 4 [2, 3, 4, (5/11)*x + 6/11]
  15 4 [2, 3, 4, (5/11)*x + 6/11]
  16 5 [2, 3, 4, 4*x - 42, (4/15)*x + 11/15]
  17 5 [2, 3, 4, 4*x - 42, (4/15)*x + 11/15]
  18 5 [2, 3, 4, 6, (4/15)*x + 11/15]

Prog

(PARI) \\ See Links section.

Crossrefs

Suggested by A373811 and A375420.

Cf. A000005, A373810, A373813, A375515 (RUNS).

Sequence in context: A300013 A130535 A329194 * A210533 A246435 A301461

Adjacent sequences: A375496 A375497 A375498 * A375500 A375501 A375502

Keyword

nonn

Author

Rémy Sigrist and N. J. A. Sloane, Aug 18 2024

Extensions

Terms a(30) onward from Max Alekseyev, Aug 18 2024

Status

approved