A328521 - OEIS

%I #37 Sep 01 2022 11:20:14

%S 1,2,4,12,24,48,240,720,5040,10080,20160,221760,665280,8648640,

%T 17297280,294053760,2205403200,27935107200,293318625600,1927522396800,

%U 8995104518400,26985313555200,782574093100800,24259796886124800,48519593772249600,1795224969573235200,8976124847866176000,368021118762513216000

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

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

%C 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

%H Amiram Eldar, <a href="/A328521/b328521.txt">Table of n, a(n) for n = 0..394</a>

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

%F 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

%t (* First load the function f at A025487, then: *)

%t 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 *)

%o (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

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

%Y Cf. also A133411.

%Y Cf. A354880.

%K nonn

%O 0,2

%A _David A. Corneth_, Jan 04 2020