A343014 - OEIS

%I #18 Apr 05 2021 03:59:41

%S 1,2,4,8,12,24,48,72,96,144,288,432,576,720,864,1152,1440,2160,2880,

%T 4320,5760,8640,12960,17280,25920,34560,43200,51840,69120,77760,86400,

%U 103680,129600,155520,172800,207360,259200,345600,388800,518400,777600,907200,1036800

%N Number with a record number of divisors whose prime factorizations contain no repeated exponents.

%C Indices of records of A181796.

%C Since A181796(n) depends only on the prime signature of n, this sequence is a subsequence of A025487.

%C 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).

%C From _David A. Corneth_, Apr 04 2021: (Start)

%C Subsequence of A087980 and of A181824.

%C 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.

%C Do we have G_m | G_(m + 1)? (End)

%H David A. Corneth, <a href="/A343014/b343014.txt">Table of n, a(n) for n = 1..700</a> (first 500 terms from Amiram Eldar)

%H Amiram Eldar, <a href="/A343014/a343014.txt">Table of n, a(n), A181796(a(n)) for n = 1..500</a>

%e 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.

%t 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

%Y Cf. A025487, A087980, A130091, A181796, A181824.

%K nonn

%O 1,2

%A _Amiram Eldar_, Apr 02 2021