A072531 Number of primes p < n such that n divided by p leaves a 1 or a composite (nonzero) remainder.

0, 0, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 3, 2, 3, 2, 3, 2, 5, 3, 5, 3, 5, 2, 6, 3, 6, 3, 6, 3, 7, 6, 5, 6, 7, 3, 7, 5, 8, 4, 8, 4, 10, 6, 8, 7, 9, 6, 10, 7, 9, 8, 11, 6, 11, 9, 10, 7, 11, 5, 14, 9, 11, 9, 11, 8, 15, 9, 13, 8, 14, 8, 14, 12, 14, 11, 15, 9, 15, 11, 14, 12, 18, 10, 16, 14, 15, 13, 16, 9

Offset: 1

Author

Amarnath Murthy, Aug 01 2002

Keywords

• nonn

Examples

			a(7) = 2: there are 2 primes viz. 2,3 which leave a remainder 1 on dividing 7.
		

Crossrefs

Cf. A072530.

Programs

Mathematica

Table[Count[PrimeQ[DeleteCases[Table[Mod[w, Prime[j]], {j, 1, PrimePi[w]}], 0]], False], {w, 1, 256}]

Extensions

More terms from Labos Elemer, Aug 02 2002

Name clarified by Felix Huber, Aug 20 2025