This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A344488 #36 May 23 2021 03:04:52
%S A344488 1,2,3,7,47,181,1307,2503,40973,46833,109177,2885373,11744311,
%T A344488 192968969,899988745
%N A344488 Numbers that start a product crescendo of record length.
%C A344488 A product crescendo is a sequence of successive integers that can be written as products j * k where the j's form a strictly increasing sequence and the k's form a strictly decreasing sequence.
%C A344488 From _Jon E. Schoenfield_, May 22 2021: (Start)
%C A344488 a(16) <= 13399626241.
%C A344488 Numbers that start long product crescendos, but are not necessarily of record length, are easy to find by testing numbers of the form 1 + m*lcm(1..k) for sufficiently large m and k. E.g., the ones that start at 13399626241 = 1 + 18592*lcm(1..16), 442452890881 = 1 + 36112*lcm(1..17), and 521688126961 = 1 + 2241*lcm(1..19) have lengths 37, 39, and 41 respectively. (End)
%C A344488 The sequence is infinite as for any n >= 0, A038507(n) starts a product crescendo of length >= n. - _Rémy Sigrist_, May 22 2021
%e A344488 181 is in the list because it begins a product crescendo that is longer than any beginning at any smaller number. Here is the crescendo:
%e A344488 1 * 181 = 181
%e A344488 2 * 91 = 182
%e A344488 3 * 61 = 183
%e A344488 4 * 46 = 184
%e A344488 5 * 37 = 185
%e A344488 6 * 31 = 186
%e A344488 11 * 17 = 187
%e A344488 47 * 4 = 188
%e A344488 63 * 3 = 189
%e A344488 95 * 2 = 190
%e A344488 191 * 1 = 191
%e A344488 This set of 11 products forms a longer crescendo than the previous record (which started at 47), and is the longest until the set of 13 products it is possible to write starting from 1307 (the next entry in the sequence).
%e A344488 Additional example: the crescendo from 2885373 (length 27) goes:
%e A344488 1 * 2885373 = 2885373
%e A344488 2 * 1442687 = 2885374
%e A344488 5 * 577075 = 2885375
%e A344488 6 * 480896 = 2885376
%e A344488 11 * 262307 = 2885377
%e A344488 19 * 151862 = 2885378
%e A344488 21 * 137399 = 2885379
%e A344488 89 * 32420 = 2885380
%e A344488 859 * 3359 = 2885381
%e A344488 1458 * 1979 = 2885382
%e A344488 4817 * 599 = 2885383
%e A344488 12437 * 232 = 2885384
%e A344488 19365 * 149 = 2885385
%e A344488 33551 * 86 = 2885386
%e A344488 93077 * 31 = 2885387
%e A344488 131154 * 22 = 2885388
%e A344488 221953 * 13 = 2885389
%e A344488 288539 * 10 = 2885390
%e A344488 320599 * 9 = 2885391
%e A344488 360674 * 8 = 2885392
%e A344488 412199 * 7 = 2885393
%e A344488 480899 * 6 = 2885394
%e A344488 577079 * 5 = 2885395
%e A344488 721349 * 4 = 2885396
%e A344488 961799 * 3 = 2885397
%e A344488 1442699 * 2 = 2885398
%e A344488 2885399 * 1 = 2885399
%o A344488 (PARI)
%o A344488 b(n)={if(n==1, 1, my(m=1); for(k=1, oo, fordiv(n+k, d, if(d>m, m=d; break)); if(m==n+k, return(k+1))))}
%o A344488 lista(lim)={my(m=0); for(n=1, lim, my(t=b(n)); if(t > m, print1(n, ", "); m=t))} \\ _Andrew Howroyd_, May 21 2021
%Y A344488 Cf. A038507.
%K A344488 nonn,hard,more
%O A344488 1,2
%A A344488 _Jon Wild_, May 20 2021
%E A344488 a(13)-a(14) from _Rémy Sigrist_, May 21 2021
%E A344488 a(15) from _Jon E. Schoenfield_, May 21 2021