cp's OEIS Frontend

This sequence is infinite since the ratio A000005(k)/A246600(k) is unbounded. For example, if k = 2^m then A000005(k)/A246600(k) = m+1.

All the terms except for 1 are in A355670.

This sequence is infinite since the ratio A000005(k)/A049419(k) is unbounded. For example, for k = A002110(m) we have A000005(k)/A049419(k) = 2^m.

The corresponding record values are 1, 2, 4, 8, 16, 32, 64, 96, 128, ...

Numbers k such that A037445(k) = 2 * A348341(k).

Numbers k such that A037445(k)/A000005(k) = 2/3. For numbers k in A036537, all the divisors are infinitary divisors, so A037445(k)/A000005(k) = 1. For numbers k that are not in A036537, the largest possible ratio A037445(k)/A000005(k) is 2/3.

Numbers whose prime factorization has exactly one exponent of the form 3*2^k-1, with k >= 0, and the rest of the exponents, if there are any, are of the form 2^k-1, with k >= 1.

The asymptotic density of this sequence is d * Sum_{p prime} (Sum_{k>=0} 1/p^(3*2^k-1))/(1 + Sum_{k>=1} 1/p^(2^k-1)) = 0.23171917985739378623..., where d = A327839.

Numbers whose prime factorization has at least one exponent that has at least two zeros in its binary representation (A158582), or at least two exponents that are not of the form 2^k-1, with k >= 1 (A062289).

The asymptotic density of this sequence is 1 - d * (1 + Sum_{p prime} (Sum_{k>=0} 1/p^(3*2^k-1))/(1 + Sum_{k>=1} 1/p^(2^k-1))) = 0.07306380398261191432..., where d = A327839.