cp's OEIS Frontend

Also, 78th powers of primes.

More generally, the n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. In this case, p = 79.

Also, 82nd powers of primes.

More generally, the n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. In this case, p = 83.

Also, 88th powers of primes.

More generally, the n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. In this case, p = 89.

A000005(a(n)) is a Fibonacci number.

The union of {1}, A001248, A030514, A030626, A030631, A137484, etc. [From R. J. Mathar, Oct 26 2009]

First differs from A374590 and A375432 at n = 25: A374590(25) = A375432(25) = 216 is not a term of this sequence.

Numbers k such that A382291(k) = 2, i.e., numbers whose number of infinitary divisors is twice the number of their unitary divisors.

Numbers whose prime factorization has a single exponent that is a sum of two distinct powers of 2 (A018900) and all the other exponents, if they exist, are powers of 2. Equivalently, numbers of the form p^e * m, where p is a prime, e is a term in A018900, and m is a term in A138302 that is coprime to p.

If k is a term then k^2 is also a term. If m is a term in A138302 that is coprime to k then k * m is also a term. The primitive terms, i.e., the terms that cannot be generated from smaller terms using these rules, are the numbers of the form p^(2^i+1), where p is prime and i >= 1.

Analogous to A060687, which is the sequence of numbers k with prime excess A046660(k) = 2.

The asymptotic density of this sequence is A271727 * Sum_{p prime} (((1 - 1/p)/f(1/p)) * Sum_{k>=1} 1/p^A018900(k)) = 0.11919967112489084407..., where f(x) = 1 - x^3 + Sum_{k>=2} (x^(2^k)-x^(2^k+1)).

a(n) = the smallest n-digit number of the form p^12 (p = prime), a(n) = 0 if no such number exists.

a(n) = the largest n-digit number of the form p^12 (p = prime), a(n) = 0 if no such number exists.

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... .

If d(j(n)) is prime p then d(a(n+1)) must be properly divisible by p. In practice the proper divisor for computation of a(n+1) toggles between d(j(n)) and d(k).

Conjecture: This is a permutation of the positive integers. Numbers with the same number (tau) of divisors appear in their natural orders (e.g., primes, semiprimes, squares).

The plot, after the first few terms, resolves itself into points tightly packed on and around a straight line of slope 1, with exceptional points appearing as significant upward or downward "spikes".

When d(j(n)) is prime p appearing for the first time in the sequence J = {d(j(a(n)), n>=1}, then a(n+1) is the smallest number with 2p divisors, which produces a significantly large upward spike above the straight line (6, 12, 48, 192, 3072, 12288, ...).

When d(j(a(n)) is 2p, seen for the first time in J, then a(n+1) is the smallest number with p divisors, which produces a large downward spike, below the straight line (2, 4, 16, 64, 1024, 4096, ...).

The sequence of fixed points starts: 1, 46, 69, 74, 110, 140, 142, 152, 154, 178, ... apparently becoming denser as n increases.