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

0,2

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

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

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 *)

Prog

(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

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.

Sequence in context: A340137 A348092 A343458 * A133411 A201078 A004645

Adjacent sequences: A328518 A328519 A328520 * A328522 A328523 A328524

Keyword

nonn

Author

David A. Corneth, Jan 04 2020

Status

approved