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

Author

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

Keywords

• nonn

Examples

			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]
		

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]

Crossrefs

Suggested by A373811 and A375420.

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

Programs

PARI

\\ See Links section.

Extensions

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