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Number of primes not exceeding sum of divisors of n.
10

%I #14 Sep 08 2022 08:45:06

%S 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,

%T 20,11,18,15,16,15,24,12,17,16,24,13,24,14,23,21,20,15,30,16,24,20,25,

%U 16,30,20,30,22,24,17,39,18,24,27,31,23,34,19,30,24,34,20,44,21,30,30

%N Number of primes not exceeding sum of divisors of n.

%H Vincenzo Librandi, <a href="/A070803/b070803.txt">Table of n, a(n) for n = 1..5000</a>

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

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

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

%o (Sage) [prime_pi(sigma(n,1)) for n in range(1, 76)] # - _Zerinvary Lajos_, Jun 06 2009

%o (PARI) A070803(n) = primepi(sigma(n)) \\ _Michael B. Porter_, Jan 28 2010

%o (Magma) [#PrimesUpTo(SumOfDivisors(n)): n in [1..100]]; // _Vincenzo Librandi_, Feb 06 2017

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

%K easy,nonn

%O 1,2

%A _Labos Elemer_, May 08 2002