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A382208 Numbers k for which pi(bigomega(k)) = omega(k).

%I A382208 #22 Apr 05 2025 15:27:00
%S A382208 1,4,9,12,18,20,24,25,28,36,40,44,45,49,50,52,54,56,63,68,75,76,88,92,
%T A382208 98,99,100,104,116,117,120,121,124,135,136,147,148,152,153,164,168,
%U A382208 169,171,172,175,180,184,188,189,196,207,212,225,232,236,240,242,244,245
%N A382208 Numbers k for which pi(bigomega(k)) = omega(k).
%C A382208 Numbers k for which A000720(A001222(k)) = A001221(k).
%C A382208 Numbers k = p_1^e_1 * ... * p_j^e_j for which pi(Sum_{i=1..j} e_i) = j where pi = A000720.
%C A382208 Supersequence of A001248, A054753, A065036, A085986, A162143, A179643, A179644, A179693, A179700, A179704.
%H A382208 Felix Huber, <a href="/A382208/b382208.txt">Table of n, a(n) for n = 1..10000</a>
%e A382208 240 = 2^4*3*5 is in the sequence because pi(Omega(240)) = pi(6) = 3 = omega(240).
%p A382208 with(NumberTheory):
%p A382208 A382208:=proc(n)
%p A382208     option remember;
%p A382208     local k;
%p A382208     if n=1 then
%p A382208         1
%p A382208     else
%p A382208         for k from procname(n-1)+1 do
%p A382208             if pi(Omega(k))=Omega(k,distinct) then
%p A382208                 return k
%p A382208             fi
%p A382208         od
%p A382208     fi;
%p A382208 end proc;
%p A382208 seq(A382208(n),n=1..59);
%p A382208 # second Maple program:
%p A382208 q:= n-> (l-> is(numtheory[pi](add(i[2], i=l))=nops(l)))(ifactors(n)[2]):
%p A382208 select(q, [$1..245])[];  # _Alois P. Heinz_, Apr 05 2025
%t A382208 Select[Range[250], PrimePi[PrimeOmega[#]] == PrimeNu[#] &] (* _Amiram Eldar_, Apr 05 2025 *)
%o A382208 (PARI) isok(k) = primepi(bigomega(k)) == omega(k); \\ _Michel Marcus_, Apr 05 2025
%Y A382208 Cf. A000720, A001221, A001222, A001248, A046386, A054753, A065036, A085986, A162143, A179644, A179693, A179700, A179704.
%K A382208 nonn
%O A382208 1,2
%A A382208 _Felix Huber_, Mar 30 2025
%E A382208 a(1) inserted by _Michel Marcus_, Apr 05 2025