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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).
5
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, 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.
Sequence in context: A300013 A130535 A329194 * A210533 A246435 A301461
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(30) onward from Max Alekseyev, Aug 18 2024
STATUS
approved