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

1,2

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(Sage) [prime_pi(sigma(n, 1)) for n in range(1, 76)] # - Zerinvary Lajos, Jun 06 2009
(PARI) A070803(n) = primepi(sigma(n)) \\ Michael B. Porter, Jan 28 2010
(Magma) [#PrimesUpTo(SumOfDivisors(n)): n in [1..100]]; // Vincenzo Librandi, Feb 06 2017

Crossrefs

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

Sequence in context: A341947 A268353 A204900 * A071693 A225381 A007728

Adjacent sequences: A070800 A070801 A070802 * A070804 A070805 A070806

Keyword

easy,nonn

Author

Labos Elemer, May 08 2002

Status

approved