A328521 Smallest highly composite number that has n prime factors counted with multiplicity.

1, 2, 4, 12, 24, 48, 240, 720, 5040, 10080, 20160, 221760, 665280, 8648640, 17297280, 294053760, 2205403200, 27935107200, 293318625600, 1927522396800, 8995104518400, 26985313555200, 782574093100800, 24259796886124800, 48519593772249600, 1795224969573235200, 8976124847866176000, 368021118762513216000

Offset: 0

Author

David A. Corneth, Jan 04 2020

Keywords

• nonn

Comments

a(n-1) differs from A133411(n) for n in A354880.

Question: Is this sequence strictly growing? If sequence A330748 is monotonic, so is this also, and vice versa. Note that the primorial deflation sequence, A330743, is not monotonic. - Antti Karttunen, Jan 14 2020

Links

• Amiram Eldar, Table of n, a(n) for n = 0..394

Crossrefs

Cf. A001222 (bigomega), A002182 (highly composite numbers), A108951, A112778 (bigomega of HCN's), A330743 (primorial deflation), A330748 (indices in A002182).

Cf. also A133411.

Cf. A354880.

Programs

Mathematica

(* First load the function f at A025487, then: *)
Block[{s = Union@ Flatten@ f@ 17, t}, t = DivisorSigma[0, s]; s = Map[s[[FirstPosition[t, #][[1]] ]] &, Union@ FoldList[Max, t]]; t = PrimeOmega[s]; Array[s[[FirstPosition[t, #][[1]] ]] &, Max@ t + 1, 0]] (* Michael De Vlieger, Jan 12 2020 *)

PARI

a(n)=for(k=1,oo,bigomega(A2182[k])==n&&return(A2182[k])) \\ Global variable A2182 must hold a vector of values of A002182. - M. F. Hasler, Jan 08 2020

Formula

a(n) = A002182(A330748(n)) = A002182(min{k: A112778(k)=n}). - M. F. Hasler, Jan 08 2020

a(n) = A108951(A330743(n)), where A330743(n) is the first term k of A329902 for which A056239(k) = n. - Antti Karttunen, Jan 13 2020