

A237597


a(n) = {0 < k < prime(n): n divides pi(k*n)}, where pi(.) is given by A000720.


8



1, 1, 1, 2, 2, 1, 1, 3, 4, 3, 3, 3, 2, 4, 3, 3, 5, 7, 1, 3, 3, 5, 2, 5, 4, 4, 5, 5, 3, 7, 3, 2, 3, 4, 8, 4, 2, 6, 4, 5, 6, 8, 7, 2, 8, 2, 7, 1, 3, 6, 4, 6, 5, 1, 7, 4, 4, 3, 5, 6, 4, 8, 6, 5, 2, 5, 8, 4, 2, 5, 7, 5, 3, 1, 3, 2, 6, 3, 2, 4
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OFFSET

1,4


COMMENTS

Conjecture: a(n) > 0 for all n > 0.
See also A237614 for the least k > 0 with pi(k*n) divisible by n.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..2500


EXAMPLE

a(6) = 1 since pi(11*6) = 3*6 with 11 < prime(6) = 13.
a(19) = 1 since pi(33*19) = 6*19 with 33 < prime(19) = 67.
a(759) = 1 since pi(2559*759) = 191*759 with 2559 < prime(759) = 5783.


MATHEMATICA

a[n_]:=Sum[If[Mod[PrimePi[k*n], n]==0, 1, 0], {k, 1, Prime[n]1}]
Table[a[n], {n, 1, 80}]


CROSSREFS

Cf. A000040, A000720, A237578, A237598, A237612, A237614.
Sequence in context: A086623 A248736 A292508 * A034928 A280267 A161671
Adjacent sequences: A237594 A237595 A237596 * A237598 A237599 A237600


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Feb 10 2014


STATUS

approved



