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A293555 Indices of records in A243822. 3
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 (list; graph; refs; listen; history; text; internal format)
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 * A338122 A169873 A079471

Adjacent sequences:  A293552 A293553 A293554 * A293556 A293557 A293558

KEYWORD

nonn

AUTHOR

Michael De Vlieger, Oct 22 2017

STATUS

approved

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Last modified July 31 10:51 EDT 2021. Contains 346373 sequences. (Running on oeis4.)