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A250214 Number of values of k such that prime(n) divides A241601(k). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A060838 A206567 A085252 * A073423 A219180 A179952

Adjacent sequences:  A250211 A250212 A250213 * A250215 A250216 A250217

KEYWORD

nonn

AUTHOR

Eric Chen, Dec 26 2014

STATUS

approved

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Last modified February 26 21:58 EST 2020. Contains 332295 sequences. (Running on oeis4.)