cp's OEIS Frontend

Subsequence of A301517 and A374459 and first differs from them at n = 21. A301517(21) = A374459(21) = 216 is not a term of this sequence.

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

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

The asymptotic density of this sequence is (1/zeta(2)) * Sum_{p prime} 1/((p-1)*(p+1)^2) = 0.093382464285953613312...

Numbers k such that A073184(k) = A190867(k).

Numbers whose largest cubefree divisor (A007948) and cubefull part (A360540) have the same number of divisors (A000005).

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

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

1 is the only cubefree (A004709) term.

Includes the 4th powers of squarefree numbers (1 and A113849).

The 4th powers of primes (A030514) are the only terms that are prime powers (A246655).

Numbers of the for m*p^(3*2^k+1), where m is squarefree, p is prime, gcd(m, p) = 1 and omega(m) = k, are all terms. In particular, this sequence includes numbers of the form p^7*q, where p != q are primes (A179664), and numbers of the form p^13*q*r where p, q, and r are distinct primes.

The corresponding numbers of cubefree (or 3-full) divisors are 1, 3, 3, 6, 3, 6, 6, 9, 6, 6, 6, 3, 6, 6, ... .

First differs from A332785 at n = 112: A332785(112) = 360 = 2^3 * 3^2 * 5 is not a term of this sequence.

First differs from A317616 at n = 38: A317616(38) = 144 = 2*4 * 3^2 is not a term of this sequence.

Numbers k such that A375933(k) = 1.

Numbers of the form s1 * s2^e, where s1 and s2 are coprime squarefree numbers that are both larger than 1, and e >= 2.

The asymptotic density of this sequence is Sum_{e>=2} d(e) = 0.36113984820338109927..., where d(e) = Product_{p prime} (1 - 1/p^2 + 1/p^e - 1/p^(e+1)) - Product_{p prime} (1 - 1/p^(e+1)) is the asymptotic density of terms k with A051903(k) = e >= 2.

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... .