cp's OEIS Frontend

First differs from A377019 at n = 55: A377019(55) = 64 is not a term of this sequence.

First differs from A344742 at n = 62: A344742(62) = 72 is not a term of this sequence.

All the cubefree numbers (A004709) are terms. The least term that is not cubefree is a(215) = 256 = 2^8. The cubefree numbers are the terms whose number of coreful divisors is equal to their number of exponential divisors.

All the exponentially refactorable numbers (A382065) are terms. The least term that is not in A382065 is a(362) = 432 = 2^4 * 3^3. The next terms that are not in A382065 are 648, 2000, 2160, 3024, 3240, 4536, 4752, 5000, ... .

For a number k whose prime factorization is Product_{i} p_i^e_i, a coreful divisor d of k has the prime factorization Product_{i} p_i^f_i with f_i >= 1 for all i. An exponential divisor of k is a coreful divisor with the additional condition that f_i | e_i for all i.

Numbers k such that A049419(k) | A005361(k).

The criterion according to which a number belongs to this sequence depends only on the prime signature of this number: if {e_1, e_2, ... } are the exponents in the prime factorization of k then k is a term if and only if A005361(k)/A049419(k) = Product_{i} e_i/A000005(e_i) is an integer.

A number k is a term if and only if the cubefull part of k, A360540(k), is a term. Therefore, the primitive terms of this sequence are the cubefull terms, A382064.

The asymptotic density of this sequence is Sum_{n>=1} f(A382064(n)) = 0.83697905945047..., where f(n) = (1/(zeta(3)*n)) * Product_{prime p|n} (p^2/(p^2+p+1)).