A237597 a(n) = |{0 < k < prime(n): n divides pi(k*n)}|, where pi(.) is given by A000720.

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

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

Zhi-Wei 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

Zhi-Wei Sun, Feb 10 2014

Status

approved