A181805 Number of divisors of A181804(n) that are highly composite (A002182).

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, 22, 22, 21, 23, 22, 17, 23, 23, 23, 24, 25, 24, 25, 23, 23, 25, 28, 25, 27, 27, 31, 22, 27, 26, 30, 18, 29, 25, 32, 33, 28, 29, 28, 35, 25, 33, 34, 31, 31, 38, 37

Offset

1,2

Comments

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.

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Achim Flammenkamp, List of the first 1200 highly composite numbers.

Eric Weisstein's World of Mathematics, Highly composite number.

Formula

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

Example

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.

Mathematica

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 *)

Crossrefs

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

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

Sequence in context: A296834 A242642 A178041 * A369450 A212010 A366418

Adjacent sequences: A181802 A181803 A181804 * A181806 A181807 A181808

Keyword

nonn

Author

Matthew Vandermast, Nov 27 2010

Extensions

More terms from Amiram Eldar, Jun 23 2023

Status

approved