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 A292867 #12 Nov 18 2017 03:43:09
%S A292867 1,8,14,16,20,22,26,28,32,38,40,44,46,48,50,52,54,56,58,62,64,68,72,
%T A292867 78,80,86,88,92,94,96,100,108,114,122,124,126,130,132,138,144,156,160,
%U A292867 162,174,186,192,204,216,222,228,234,240,246,252,258,264,270,276,282
%N A292867 Indices of records in A243823.
%C A292867 Except for A292867(1) = 1, all terms are even.
%C A292867 Some conjectures:
%C A292867 1. The only prime powers p^e in this sequence are {8, 16, 32, 64}.
%C A292867 2. Squarefree terms m appear throughout. (There are 261 squarefree values among the first 1261 terms.)
%C A292867 3. Terms that set records for omega(m) are 1, followed by 2^e, with 3 <= e <= 6, then 2^e * 3 with 6 <= e <= 8, then 2^7 * A002110(k) with k >= 1.
%C A292867 4. Primorials A002110(n) for n >= 6 appear in this sequence. The first primorials in m are terms 6 through 8 of A002110 (i.e., 30030, 510510, 9699690) at n = 419, 774, 1258, respectively.
%C A292867 5. Outside of a(n) with 2 <= n <= 21 and n = {29, 30}, all terms of A244052 are also in this sequence. This observation applies to the smallest 104 terms of A244052.
%C A292867 6. For very large n, all terms are also in A244052. For small n, few terms of A244052 appear and are separated by many other numbers. Since numbers m in A244052 are products of k primes, many of which are the smallest primes, phi is minimized and A010846(m) becomes infinitesimal in comparison to m. Therefore A243823(m) is tantamount to the cototient of m. The size of n required to observe this agreement between this sequence and A244052 is unknown.
%H A292867 Michael De Vlieger, <a href="/A292867/b292867.txt">Table of n, a(n) for n = 1..1500</a>
%H A292867 Michael De Vlieger, <a href="/A292867/a292867.txt">Records and Indices of Records in A243823</a>
%e A292867 8 is in the sequence since it is the first number n such that A243823(n) > 0. 14 appears immediately after 8 since A243823(14) = 3, and 3 is greater than the values that precede it.
%e A292867 Table of indices a(n) of records b(n) in A243823 = n - phi(n) - A010846(n) + 1:
%e A292867 .
%e A292867 n a(n) b(n) phi(a(n)) A010846(a(n))
%e A292867 -------------------------------------
%e A292867 1 1 0 1 1
%e A292867 2 8 1 4 4
%e A292867 3 14 3 6 6
%e A292867 4 16 4 8 5
%e A292867 5 20 5 8 8
%e A292867 6 22 6 10 7
%e A292867 7 26 8 12 7
%e A292867 8 28 9 12 8
%e A292867 9 32 11 16 6
%e A292867 10 38 13 18 8
%e A292867 11 40 14 16 11
%e A292867 12 44 16 20 9
%e A292867 13 46 17 22 8
%e A292867 14 48 18 16 15
%e A292867 15 50 19 20 12
%e A292867 16 52 20 24 9
%e A292867 17 54 21 18 16
%e A292867 18 56 22 24 11
%e A292867 19 58 23 28 8
%e A292867 20 62 25 30 8
%e A292867 ...
%t A292867 With[{s = Table[Count[Range[4, n - 2], _?(Nor[CoprimeQ[#, n], PowerMod[n, Floor@ Log2@ n, #] == 0] &)], {n, 282}]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* _Michael De Vlieger_, Oct 02 2017 *)
%Y A292867 Cf. A002110, A243823, A244052, A272619, A292868.
%K A292867 nonn
%O A292867 1,2
%A A292867 _Michael De Vlieger_, Oct 02 2017