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

1, 4, 9, 12, 18, 20, 24, 25, 28, 36, 40, 44, 45, 49, 50, 52, 54, 56, 63, 68, 75, 76, 88, 92, 98, 99, 100, 104, 116, 117, 120, 121, 124, 135, 136, 147, 148, 152, 153, 164, 168, 169, 171, 172, 175, 180, 184, 188, 189, 196, 207, 212, 225, 232, 236, 240, 242, 244, 245

Offset: 1

Author

Felix Huber, Mar 30 2025

Keywords

• nonn

Comments

Numbers k for which A000720(A001222(k)) = A001221(k).

Numbers k = p_1^e_1 * ... * p_j^e_j for which pi(Sum_{i=1..j} e_i) = j where pi = A000720.

Supersequence of A001248, A054753, A065036, A085986, A162143, A179643, A179644, A179693, A179700, A179704.

Examples

			240 = 2^4*3*5 is in the sequence because pi(Omega(240)) = pi(6) = 3 = omega(240).
		

Links

• Felix Huber, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720, A001221, A001222, A001248, A046386, A054753, A065036, A085986, A162143, A179644, A179693, A179700, A179704.

Programs

Maple

with(NumberTheory):
A382208:=proc(n)
    option remember;
    local k;
    if n=1 then
        1
    else
        for k from procname(n-1)+1 do
            if pi(Omega(k))=Omega(k,distinct) then
                return k
            fi
        od
    fi;
end proc;
seq(A382208(n),n=1..59);
# second Maple program:
q:= n-> (l-> is(numtheory[pi](add(i[2], i=l))=nops(l)))(ifactors(n)[2]):
select(q, [$1..245])[];  # Alois P. Heinz, Apr 05 2025

Mathematica

Select[Range[250], PrimePi[PrimeOmega[#]] == PrimeNu[#] &] (* Amiram Eldar, Apr 05 2025 *)

PARI

isok(k) = primepi(bigomega(k)) == omega(k); \\ Michel Marcus, Apr 05 2025

Extensions

a(1) inserted by Michel Marcus, Apr 05 2025