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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).

%I A375499 #26 Oct 20 2024 23:35:55
%S A375499 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,
%T A375499 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,
%U A375499 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
%N 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).
%H A375499 Max Alekseyev, <a href="/A375499/b375499.txt">Table of n, a(n) for n = 1..400</a>
%H A375499 Max Alekseyev, <a href="https://github.com/maxale/oeis/blob/main/a3738xx_lines_covering_points.sage">Sage program for lines covering points</a>, Github, Aug 19 2024
%H A375499 Rémy Sigrist, <a href="/A375499/a375499.gp.txt">PARI program</a>
%H A375499 N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=3RAYoaKMckM">A Nasty Surprise in a Sequence and Other OEIS Stories</a>, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane85BD.pdf">Slides</a> [Mentions this sequence]
%e A375499 The initial terms, together with an appropriate set of lines, are:
%e A375499   1 1 [1]
%e A375499   2 1 [x]
%e A375499   3 2 [2, x]
%e A375499   4 2 [2, (2/3)*x + 1/3]
%e A375499   5 2 [2, (2/3)*x + 1/3]
%e A375499   6 3 [2, 2*x - 8, (2/3)*x + 1/3]
%e A375499   7 3 [2, 2*x - 8, (2/3)*x + 1/3]
%e A375499   8 3 [2, 4, (2/3)*x + 1/3]
%e A375499   9 4 [2, 3, 4, x]
%e A375499   10 4 [2, 3, 4, x]
%e A375499   11 4 [2, 3, 4, x]
%e A375499   12 4 [2, 3, 4, (5/11)*x + 6/11]
%e A375499   13 4 [2, 3, 4, (5/11)*x + 6/11]
%e A375499   14 4 [2, 3, 4, (5/11)*x + 6/11]
%e A375499   15 4 [2, 3, 4, (5/11)*x + 6/11]
%e A375499   16 5 [2, 3, 4, 4*x - 42, (4/15)*x + 11/15]
%e A375499   17 5 [2, 3, 4, 4*x - 42, (4/15)*x + 11/15]
%e A375499   18 5 [2, 3, 4, 6, (4/15)*x + 11/15]
%o A375499 (PARI) \\ See Links section.
%Y A375499 Suggested by A373811 and A375420.
%Y A375499 Cf. A000005, A373810, A373813, A375515 (RUNS).
%K A375499 nonn
%O A375499 1,3
%A A375499 _Rémy Sigrist_ and _N. J. A. Sloane_, Aug 18 2024
%E A375499 Terms a(30) onward from _Max Alekseyev_, Aug 18 2024