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A343014 Number with a record number of divisors whose prime factorizations contain no repeated exponents. 1
1, 2, 4, 8, 12, 24, 48, 72, 96, 144, 288, 432, 576, 720, 864, 1152, 1440, 2160, 2880, 4320, 5760, 8640, 12960, 17280, 25920, 34560, 43200, 51840, 69120, 77760, 86400, 103680, 129600, 155520, 172800, 207360, 259200, 345600, 388800, 518400, 777600, 907200, 1036800 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Indices of records of A181796.
Since A181796(n) depends only on the prime signature of n, this sequence is a subsequence of A025487.
The corresponding record values are 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 19, 20, 21, 22, ... (see the link for more values).
From David A. Corneth, Apr 04 2021: (Start)
Subsequence of A087980 and of A181824.
Let G_m be the gcd of terms k with omega(k) = m. So G_1 <= 2, G_2 <= 12, G_3 <= 720, G_4 <= 907200.
Do we have G_m | G_(m + 1)? (End)
LINKS
David A. Corneth, Table of n, a(n) for n = 1..700 (first 500 terms from Amiram Eldar)
EXAMPLE
A181796 begins with 1, 2, 2, 3, 2, 3, 2, 4, .... The record values, 1, 2, 3 and 4 occur at 1, 2, 4 and 8, which are the first 4 terms of this sequence.
MATHEMATICA
q[n_] := UnsameQ @@ FactorInteger[n][[;; , 2]]; s[n_] := DivisorSum[n, 1 &, q[#] &]; sm = 0; seq = {}; Do[s1 = s[n]; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 1, 10^4}]; seq
CROSSREFS
Sequence in context: A279312 A326076 A181808 * A097942 A354541 A358513
KEYWORD
nonn
AUTHOR
Amiram Eldar, Apr 02 2021
STATUS
approved

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Last modified March 28 11:46 EDT 2024. Contains 371241 sequences. (Running on oeis4.)