A293555 Indices of records in A243822.

1, 6, 10, 18, 30, 42, 60, 78, 84, 90, 126, 150, 210, 330, 390, 420, 630, 840, 990, 1050, 1470, 1890, 2100, 2310, 2730, 3570, 3990, 4620, 5460, 6930, 8190, 9240, 10920, 11550, 13650, 13860, 16170, 19110, 20790, 23100, 25410, 30030, 39270, 43890, 46410, 51870

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

Cf. A000005, A010846, A243822, A244052, A272618, A293556.

Sequence in context: A248056 A331861 A032641 * A077626 A338122 A169873

Adjacent sequences: A293552 A293553 A293554 * A293556 A293557 A293558

Keyword

nonn

Author

Michael De Vlieger, Oct 22 2017

Status

approved