A250214 Number of values of k such that prime(n) divides A241601(k).

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 1, 1, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 1, 1, 2, 0, 1, 1, 0, 1, 1, 3, 3, 0, 0, 0, 0, 1, 2, 3, 1, 0, 1, 3, 0, 1, 0, 1, 1, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 1, 0, 1, 2, 2, 1, 2, 0, 1, 3, 3, 1, 0, 0, 1, 1, 3, 3, 2, 0, 0, 3, 1, 1

Offset

1,19

Comments

a(n) is called the weak irregular index of n-th prime, that is, the Bernoulli irregular index + Euler irregular index.

Prime(n) is a regular prime if and only if a(n) = 0.

Does every natural number appear in this sequence? For example, for the primes 491 and 1151, a(94) = a(190) = 4. (491 and 1151 are the only primes below 1800 with weak irregular index 4 or more.) However, does a(n) have a limit?

Links

Table of n, a(n) for n=1..120.

Eric Weisstein's World of Mathematics, Irregular Pair

Example

a(8) = 1 since the 8th prime is 19, which divides A241601(11).
a(13) = 0 since the 13th prime is 41, a regular prime.
a(19) = 2 since the 19th prime is 67, which divides both A241601(27) and A241601(58).

Crossrefs

Cf. A091888, A091887, A250216, A000928, A120337, A128197, A250213.

Sequence in context: A206567 A362422 A085252 * A073423 A219180 A179952

Adjacent sequences: A250211 A250212 A250213 * A250215 A250216 A250217

Keyword

nonn

Author

Eric Chen, Dec 26 2014

Status

approved