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A250214 Number of values of k such that prime(n) divides A241601(k). 1

%I

%S 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,

%T 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,

%U 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

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

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

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

%C 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?

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IrregularPair.html">Irregular Pair</a>

%e a(8) = 1 since the 8th prime is 19, which divides A241601(11).

%e a(13) = 0 since the 13th prime is 41, a regular prime.

%e a(19) = 2 since the 19th prime is 67, which divides both A241601(27) and A241601(58).

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

%K nonn

%O 1,19

%A _Eric Chen_, Dec 26 2014

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Last modified April 5 00:43 EDT 2020. Contains 333238 sequences. (Running on oeis4.)