A072530 Number of primes p < n such that n divided by p leaves a prime remainder.

0, 0, 0, 0, 1, 0, 1, 2, 1, 1, 1, 2, 2, 2, 1, 3, 3, 3, 2, 3, 1, 3, 3, 5, 2, 4, 2, 4, 3, 4, 3, 4, 4, 3, 2, 6, 4, 5, 2, 6, 4, 6, 3, 6, 4, 5, 5, 7, 4, 6, 4, 5, 4, 8, 3, 5, 4, 7, 5, 9, 3, 7, 5, 8, 5, 7, 3, 8, 4, 8, 5, 10, 6, 7, 5, 8, 4, 9, 6, 9, 7, 8, 4, 10, 5, 7, 6, 8, 7, 12, 5, 8, 8, 8, 5, 12, 6, 10, 5, 10, 5

Offset: 1

Author

Amarnath Murthy, Aug 01 2002

Keywords

• nonn

Comments

Is there any n > 6 such that a(n) = 0?

Examples

			a(17) = 3: there are 3 primes viz. 3, 5 and 7 which leave prime remainders on dividing 17.
		

Crossrefs

Cf. A072531.

Programs

Mathematica

Table[Count[PrimeQ[Table[Mod[w, Prime[j]], {j, 1, PrimePi[w]}]], True], {w, 1, 256}]

Extensions

More terms from Labos Elemer, Aug 02 2002

Name clarified by Felix Huber, Aug 20 2025