
COMMENTS

Inspired by A278348.
Index of first occurrence of k >= 0, or zero if no such number exists: 1, 9, 6, 0, 10, 0, 14, 16, 12, 0, 22, 0, 21, 18, 0, 49, 20, 0, 38, 0, 33, 0, 46, 32, 28, 0, ..., ;
Numbers which never occur: 3, 5, 9, 11, 14, 17, 19, 21, 25, 27, 29, 31, 33, 34, 35, 37, 39, 41, 43, 47, 51, ..., ;
Records: 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, 22048, ..., ;
which first occur for n: 0, 6, 10, 12, 18, 20, 24, 30, 36, 40, 42, 48, 56, 60, 72, 84, 90, 108, 120, 144, 168, 180, 210, 240, 280, 300, 330, 336, 360, 420, 480, 504, 540, 600, 630, 660, 720, 840, 1008, 1080, 1200, 1260, 1440, 1560, 1680, 1980, 2100, 2160, 2310, 2340, 2520, ..., .
If instead we look for the number of unordered ways two distinct elements {a, b) of S satisfy a*b = n, then a(n) = floor(sigma_0(n)  2)) = A211159(n+1).
Number of 2 X 2 singular matrices of the form
[c a]
[b n]
with a, b, and c distinct positive integers less than n and a < b.
