cp's OEIS Frontend

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

%I A328521 #37 Sep 01 2022 11:20:14
%S A328521 1,2,4,12,24,48,240,720,5040,10080,20160,221760,665280,8648640,
%T A328521 17297280,294053760,2205403200,27935107200,293318625600,1927522396800,
%U A328521 8995104518400,26985313555200,782574093100800,24259796886124800,48519593772249600,1795224969573235200,8976124847866176000,368021118762513216000
%N A328521 Smallest highly composite number that has n prime factors counted with multiplicity.
%C A328521 a(n-1) differs from A133411(n) for n in A354880.
%C A328521 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 A328521 Amiram Eldar, <a href="/A328521/b328521.txt">Table of n, a(n) for n = 0..394</a>
%F A328521 a(n) = A002182(A330748(n)) = A002182(min{k: A112778(k)=n}). - _M. F. Hasler_, Jan 08 2020
%F A328521 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 A328521 (* First load the function f at A025487, then: *)
%t A328521 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 A328521 (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 A328521 Cf. A001222 (bigomega), A002182 (highly composite numbers), A108951, A112778 (bigomega of HCN's), A330743 (primorial deflation), A330748 (indices in A002182).
%Y A328521 Cf. also A133411.
%Y A328521 Cf. A354880.
%K A328521 nonn
%O A328521 0,2
%A A328521 _David A. Corneth_, Jan 04 2020