A237597 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(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.