cp's OEIS Frontend

First differs from A138302 and A270428 at n = 57: a(57) = 64 is not a term of A138302 and A270428.

First differs from A337052 at n = 193: A337052(193) = 216 is not a term of this sequence.

First differs from A335275 at n = 227: A335275(227) = 256 is not a term of this sequence.

First differs from A220218 at n = 903: A220218(903) = 1024 is not a term of this sequence.

Numbers k such that A376886(k) = A001221(k).

The asymptotic density of this sequence is Product_{p prime} (1 - 1/p^3 + (1 - 1/p) * (Sum_{k>=3} 1/p^A051683(k))) = 0.87902453718626485582... .

a(n) = A096432(n-1) for 2<=n<380, but then the sequences start to differ: A096432 contains 432, 648, 1024, 1728, 2000, 2160,... which are not in this sequence. - R. J. Mathar, Oct 15 2024

First differs from its subsequence A046100 at n = 61: a(61) = 64 is not a term of A046100.

Numbers k such that A376885(k) = A376886(k).

Numbers that are "squarefree" when they are factorized into factors of the form p^(k!), where p is a prime and k >= 1, a factorization that is done using the factorial-base representation of the exponents in the prime factorization (see A376885 for more details). Each factor p^(k!) has a multiplicity 1.

The asymptotic density of this sequence is Product_{p prime} (1 - 1/p^2 + (1 - 1/p) * (Sum_{k>=2} 1/p^A059590(k))) = 0.93973112474919498992... .

Numbers that are "powerful" when they are factorized into factors of the form p^(k!), where p is a prime and k >= 1, a factorization that is done using the factorial-base representation of the exponents in the prime factorization (see A376885 for more details). Each factor p^(k!) has a multiplicity that is larger than 1.

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)).

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.

Subsequence of A382063 and first differs from it at n = 362: A382063(362) = 432 = 2^4 * 3^3 is not a term of this sequence.

The asymptotic density of this sequence is Product_{p prime} (1 - 1/p^3 + (1 - 1/p) * (Sum_{k>=3} 1/p^A033950(k))) = 0.83493143539605138255... .

The relative density of this sequence within A382063 is the ratio between the densities of the two sequences: 0.997553... .