OFFSET
1,2
COMMENTS
From Michael De Vlieger, Nov 17 2017: (Start)
Terms in a(n) appear in A244052 except {78, 126, 990, 19110, 6276270, ...}.
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.
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).
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).
(End)
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..110
Michael De Vlieger, Records and indices of records in A243822
EXAMPLE
From Michael De Vlieger, Nov 17 2017: (Start)
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).
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.
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.
a(3) = 10 since it has 2 such k (i.e., 4 | 10^2, 8 | 10^3), etc.
(End)
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Oct 22 2017
STATUS
approved