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 A334238 #15 May 03 2020 16:22:14
%S A334238 57,63,171,258,266,294,301,329,342,343,354,361,377,378,379,381,387,
%T A334238 399,423,437,441,462,463,469,474,481,483,489,506,513,529,567,603,621,
%U A334238 642,643,689,798,817,889,903,931,978,1026,1083,1141,1143,1161,1169,1197,1204
%N A334238 Rows n in A334184 that are not unimodal.
%C A334238 Consider the mappings k -> (k - (k/p)), across primes p | k. a(n) = rank levels of antichains in the poset resulting from taking distinct terms generated by the mapping and preserving the order of their generation.
%C A334238 We deem a series of rank levels, such as those of n = 15, i.e., row 15 of A334184 = [1, 2, 3, 2, 1, 1], as unimodal, as the terms increase to a point, then decrease.
%C A334238 Early terms may suggest that 2^i +/- 1 appear often in a(n). Given 10000 terms, the only such instances are {63, 513, 2047, 16383} for i = {6, 9, 11, 14}.
%C A334238 a(n) for 1 <= n <= 710 are bimodal. Are there rows n > 710 in A334184 that increase and decrease more than twice?
%H A334238 Peter Kagey, <a href="/A334238/b334238.txt">Table of n, a(n) for n = 1..10000</a>
%H A334238 Michael De Vlieger <a href="https://oeis.org/A334184/a334184.png">Hasse diagrams</a> of the 24 least terms of this sequence.
%e A334238 Example: n = 57 is the smallest number for which rank levels of antichains is not unimodal, under the poset formed from distinct terms resulting from the mapping f(n) := n -> n - n/p across primes p | n.
%e A334238 Hasse diagram Row 57 of A334184
%e A334238 ------------- -----------------
%e A334238 57 1
%e A334238 | \
%e A334238 | \
%e A334238 54 38 2
%e A334238 | \/ \
%e A334238 | /\ \
%e A334238 36 27 19 3
%e A334238 | \ | /
%e A334238 | \| /
%e A334238 24 18 2
%e A334238 /| /|
%e A334238 / | / |
%e A334238 16 12 9 3
%e A334238 | /| /
%e A334238 |/ |_/
%e A334238 8 6 2
%e A334238 | /|
%e A334238 |/ |
%e A334238 4 3 2
%e A334238 | /
%e A334238 |/
%e A334238 2 1
%e A334238 |
%e A334238 |
%e A334238 1 1
%t A334238 Select[Range[2, 600], Function[k, Which[IntegerQ@ Log2@ k, False, And[PrimeQ@ k, IntegerQ@ Log2[k - 1]], False, True, ! AllTrue[Drop[#, FirstPosition[#, _?(# < 0 &)][[1]] - 1 ], # <= 0 &] &@ Sign@ Differences@ Map[Length@ Union@ # &, Transpose@ If[k == 1, {{1}}, NestWhile[If[Length[#] == 0, Map[{k, #} &, # - # /FactorInteger[#][[All, 1]] ], Union[Join @@ Map[Function[{w, n}, Map[Append[w, If[n == 0, 0, n - n/#]] &, FactorInteger[n][[All, 1]] ]] @@ {#, Last@ #} &, #]] ] &, k, If[ListQ[#], AllTrue[#, Last[#] > 1 &], # > 1] &]]]]]]
%Y A334238 Cf. A334184.
%K A334238 nonn
%O A334238 1,1
%A A334238 _Michael De Vlieger_, _Peter Kagey_, _Antti Karttunen_, Apr 19 2020