cp's OEIS Frontend

Numbers k such that A034444(k) = A005361(k).

Numbers whose squarefree kernel (A007947) and powerful part (A057521) have the same number of divisors (A000005).

If k and m are coprime terms, then k*m is also a term.

All the terms are exponentially 2^n-numbers (A138302).

The characteristic function of this sequence depends only on prime signature.

Numbers whose canonical prime factorization has exponents whose geometric mean is 2.

Equivalently, numbers of the form Product_{i=1..m} p_i^(2^k_i), where p_i are distinct primes, and Sum_{i=1..m} k_i = m (i.e., the exponents k_i have an arithmetic mean 1).

1 is the only squarefree (A005117) term.

Includes the squares of squarefree numbers (A062503), which are the powerful (A001694) terms of this sequence.

The squares of primes (A001248) are the only terms that are prime powers (A246655).

Numbers of the for m*p^(2^k), where m is squarefree, p is prime, gcd(m, p) = 1 and omega(m) = k - 1, are all terms. In particular, this sequence includes numbers of the form p^4*q, where p != q are primes (A178739), and numbers of the form p^8*q*r where p, q, and r are distinct primes (A179747).

The corresponding numbers of squarefree (or powerful) divisors are 1, 2, 2, 2, 4, 4, 2, 4, 4, 4, 2, 4, ... . The least term with 2^k squarefree divisors is A360903(k).

Numbers k whose largest unitary divisor that is a square, A350388(k), is a prime power (A246655), or equivalently, A350388(k) is in A056798 \ {1}.

Numbers having exactly one non-unitary prime factor and its multiplicity is even.

Numbers whose prime signature (A118914) is of the form {1, 1, ..., 2*m} with m >= 1, i.e., any number (including zero) of 1's and then a single even number.

The asymptotic density of this sequence is (1/zeta(2)) * Sum_{p prime} p/((p-1)*(p+1)^2) = 0.24200684327095676029... .

First differs from A344653 and A345193 at n = 17: a(17) = 120 is not a term of these sequences.

Numbers whose prime signature (A118914) is of the form {1, 1, ..., m} with m >= 3, i.e., any number (including zero) of 1's and then a single number >= 3.

The asymptotic density of this sequence is (1/zeta(2)) * Sum_{p prime} 1/(p*(p^2-1)) = A369632 / A013661 = 0.13463358553764438661... .