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

Offset: 1

Author

Zhi-Wei Sun, Feb 10 2014

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A000720, A237578, A237597, A237598, A237612.

Programs

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}]