A181805 - OEIS

%I #12 Jun 23 2023 03:42:14

%S 1,2,3,3,5,6,6,7,6,7,8,8,8,10,11,14,9,9,12,14,19,15,20,21,21,20,15,22,

%T 22,22,21,23,22,17,23,23,23,24,25,24,25,23,23,25,28,25,27,27,31,22,27,

%U 26,30,18,29,25,32,33,28,29,28,35,25,33,34,31,31,38,37

%N Number of divisors of A181804(n) that are highly composite (A002182).

%C a(n) = maximal number of members of A002182 that have a least common multiple of A181804(n). Also, a(n) = length of row A181804(n) in triangles A181802 and A181803.

%C 4, 13 and 16 are the first three positive integers that appear nowhere in this sequence (and, therefore, nowhere in A181801).  It would be interesting to know whether there are others.

%H Amiram Eldar, <a href="/A181805/b181805.txt">Table of n, a(n) for n = 1..10000</a>

%H Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/highly.txt">List of the first 1200 highly composite numbers</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HighlyCompositeNumber.html">Highly composite number</a>.

%F a(n) = A181801(A181804(n)).

%e A181804(10) = 72 has exactly seven divisors that are members of A002182 (namely, 1, 2, 4, 6, 12, 24 and 36). Hence, a(10) = 7.

%t seq[max_] := Module[{hcn = {}, hcnmax, d, dm = 0, s = {1}}, Do[d = DivisorSigma[0, n]; If[d > dm, dm = d; AppendTo[hcn, n]], {n, 1, max}]; hcnmax = hcn[[-1]]; Do[s = Union[Join[s, Select[LCM[hcn[[k]], s], # <= hcnmax &]]], {k, 2, Length[hcn]}]; Do[s[[k]] = Count[hcn, _?(Divisible[s[[k]], #] &)], {k, 1, Length[s]}]; s]; seq[300000] (* _Amiram Eldar_, Jun 23 2023 *)

%Y A181806(m) is the m-th member of A181804 such that the value of a(n) increases to a record. See also A181807.

%Y Cf. A002182, A181801, A181802, A181803, A181804.

%K nonn

%O 1,2

%A _Matthew Vandermast_, Nov 27 2010

%E More terms from _Amiram Eldar_, Jun 23 2023