A350113 a(1)=1; for n>1 a(n) is the smallest highly composite number (A002182) that is a multiple of a(n-1) where the ratios are strictly increasing.

1, 2, 6, 24, 120, 720, 5040, 45360, 498960, 6486480, 110270160, 2095133040, 41902660800, 963761198400, 26985313555200, 782574093100800, 24259796886124800, 897612484786617600, 36802111876251321600, 1582490810678806828800, 74377068101903920953600, 3941984609400907810540800

Offset

1,2

Comments

Known ratios are 2,3,4,5,6,7,9,11,13,17,19,20,23,28,29,31,37,41,43,47,53.

Links

Table of n, a(n) for n=1..22.

Example

a(2) is 2 because 1*2=2 is highly composite.
a(3) is 6 because 2*3=6 is highly composite.
a(8) cannot be 5040*8=40320 because 40320 is not a highly composite number.

Mathematica

hcn = Import["https://oeis.org/A002182/b002182.txt", "Table"][[;; , 2]]; seq = {1}; m = ratio = ratioPrev = 1; Do[k = FirstCase[hcn, _?(Divisible[#, m] && (ratio = #/m) > ratioPrev &)]; AppendTo[seq, k]; m = k; ratioPrev = ratio, {21}]; seq (* Amiram Eldar, Dec 16 2021 *)

Crossrefs

Cf. A002182.

Sequence in context: A370360 A074166 A130641 * A129655 A114796 A265086

Adjacent sequences: A350110 A350111 A350112 * A350114 A350115 A350116

Keyword

nonn

Author

J. Lowell, Dec 14 2021

Extensions

More terms from Amiram Eldar, Dec 14 2021

Status

approved