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A136033 a(n) = smallest number k such that number of prime factors of 2^k-1 is exactly n (counted with multiplicity).

%I A136033 #31 May 25 2025 19:26:34
%S A136033 2,4,6,16,12,18,24,40,54,36,102,110,60,72,108,140,120,156,144,200,216,
%T A136033 210,240,180,456,288,336,300,396,480,882,360,468,700
%N A136033 a(n) = smallest number k such that number of prime factors of 2^k-1 is exactly n (counted with multiplicity).
%p A136033 N:= 24: # to get a(1) to a(N)
%p A136033 unknown:= N:
%p A136033 for k from 2 while unknown > 0 do
%p A136033   q:= numtheory:-bigomega(2^k-1);
%p A136033   if q <= N and not assigned(A[q]) then
%p A136033      A[q]:= k;
%p A136033      unknown:= unknown - 1;
%p A136033   fi
%p A136033 od:
%p A136033 seq(A[i],i=1..N); # _Robert Israel_, Oct 24 2014
%t A136033 Module[{nn=250,tbl},tbl=Table[{k,PrimeOmega[2^k-1]},{k,nn}];Table[SelectFirst[tbl,#[[2]]==n&],{n,24}]][[;;,1]] (* The program generates the first 24 terms of the sequence. *)  (* _Harvey P. Dale_, May 25 2025 *)
%o A136033 (PARI) a(n) = {k = 1; while(bigomega(2^k-1) != n, k++); k;} \\ _Michel Marcus_, Nov 04 2013
%Y A136033 Cf. A000225, A003260, A016047, A046051, A049479, A088863, A136030, A136031.
%K A136033 nonn,more,hard
%O A136033 1,1
%A A136033 _Artur Jasinski_, Dec 11 2007
%E A136033 a(15)-a(20) from _Michel Marcus_, Nov 04 2013
%E A136033 a(21)-a(24) from _Derek Orr_, Oct 23 2014
%E A136033 a(25)-a(34) from _Jinyuan Wang_, Jun 07 2019