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 A293555 #11 Nov 18 2017 06:34:17
%S A293555 1,6,10,18,30,42,60,78,84,90,126,150,210,330,390,420,630,840,990,1050,
%T A293555 1470,1890,2100,2310,2730,3570,3990,4620,5460,6930,8190,9240,10920,
%U A293555 11550,13650,13860,16170,19110,20790,23100,25410,30030,39270,43890,46410,51870
%N A293555 Indices of records in A243822.
%C A293555 From _Michael De Vlieger_, Nov 17 2017: (Start)
%C A293555 Terms in a(n) appear in A244052 except {78, 126, 990, 19110, 6276270, ...}.
%C A293555 Primorials A002110(t) seem to divide this sequence into "tiers" thus: all terms A002110(t) <= m < A002110(t + 1), wherein A001221(m) = t as seen in A244052.
%C A293555 Terms in A244052 appear in a(n) except {2, 4, 12, 24, 120, 180, 1260, 1680, 18480, 27720, 360360, ...}. These numbers seem to have significantly more divisors than terms that are slightly greater or lesser in a(n).
%C A293555 Conjecture: all terms of a(n) with n > 92 also appear in A244052, and all terms in A244052 greater than a(92) = 6276270 appear in a(n).
%C A293555 (End)
%H A293555 Michael De Vlieger, <a href="/A293555/b293555.txt">Table of n, a(n) for n = 1..110</a>
%H A293555 Michael De Vlieger, <a href="/A293555/a293555.txt">Records and indices of records in A243822</a>
%e A293555 From _Michael De Vlieger_, Nov 17 2017: (Start)
%e A293555 Consider A243822(n), a function that counts numbers k < n such that k | n^e with e >= 2. The numbers k themselves appear in A272618(n).
%e A293555 a(1) = 1 since the number 1 has 0 such k. Primes p also have 0 such k, since 1 | p and all other numbers k < p are coprime to p. Prime powers p^e have 0 such k since any number k | n^e divides n^1.
%e A293555 a(2) = 6 since it is the smallest number to have 1 such k (i.e., 4 | 6^2). The numbers 7, 8, and 9 are prime powers having 0 such k.
%e A293555 a(3) = 10 since it has 2 such k (i.e., 4 | 10^2, 8 | 10^3), etc.
%e A293555 (End)
%t A293555 With[{s = Table[Count[Range@ n, _?(PowerMod[n, #, #] == 0 &)] - DivisorSigma[0, n], {n, 10^4}]}, Position[s, #][[1, 1]] & /@ Union@ FoldList[Max, s]] (* _Michael De Vlieger_, Oct 22 2017 *)
%Y A293555 Cf. A000005, A010846, A243822, A244052, A272618, A293556.
%K A293555 nonn
%O A293555 1,2
%A A293555 _Michael De Vlieger_, Oct 22 2017