A237614 - OEIS

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A237614

Least positive integer k with A000720(k*n) divisible by n, or 0 if such a number k does not exist.

1, 2, 2, 2, 6, 11, 11, 7, 3, 3, 3, 8, 13, 13, 8, 14, 14, 14, 33, 33, 9, 15, 9, 4, 4, 42, 22, 22, 43, 4, 36, 99, 10, 10, 10, 10, 38, 38, 38, 38, 31, 24, 17, 17, 17, 62, 24, 194, 55, 80, 11, 40, 11, 11, 11, 11, 11, 57, 11, 11, 33, 18, 18, 83, 164, 5, 5, 5, 156, 5

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OFFSET

1,2

COMMENTS

According to the conjecture in A237597, we should always have 0 < a(n) < prime(n).

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

EXAMPLE

a(3) = 2 since pi(2*3) = 3 is divisible by 3, but pi(1*3) = 2 is not.

MATHEMATICA

Do[Do[If[Mod[PrimePi[k*n], n]==0, Print[n, " ", k]; Goto[aa]], {k, 1, Prime[n]-1}];

Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 70}]