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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 12 08:23 EDT 2020. Contains 335657 sequences. (Running on oeis4.)