A070803 Number of primes not exceeding sum of divisors of n.

0, 2, 2, 4, 3, 5, 4, 6, 6, 7, 5, 9, 6, 9, 9, 11, 7, 12, 8, 13, 11, 11, 9, 17, 11, 13, 12, 16, 10, 20, 11, 18, 15, 16, 15, 24, 12, 17, 16, 24, 13, 24, 14, 23, 21, 20, 15, 30, 16, 24, 20, 25, 16, 30, 20, 30, 22, 24, 17, 39, 18, 24, 27, 31, 23, 34, 19, 30, 24, 34, 20, 44, 21, 30, 30

Offset: 1

Author

Labos Elemer, May 08 2002

Keywords

• easy
• nonn

Examples

			n=50: sigma(50) = 93, pi(93) = 24 = a(50).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A007818, A000203, A000720, A070800-A070804.

Programs

Magma

[#PrimesUpTo(SumOfDivisors(n)): n in [1..100]]; // Vincenzo Librandi, Feb 06 2017

Mathematica

Table[PrimePi[DivisorSigma[1, n]], {n, 1, 256}]

PARI

A070803(n) = primepi(sigma(n)) \\ Michael B. Porter, Jan 28 2010

Sage

[prime_pi(sigma(n,1)) for n in range(1, 76)] # - Zerinvary Lajos, Jun 06 2009

Formula

a(n) = A000720(A000203(n)) = pi(sigma(n)).