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A062700 Terms of A000203 that are prime.

%I A062700 #27 Sep 08 2022 08:45:03
%S A062700 3,7,13,31,31,127,307,1093,1723,2801,3541,8191,5113,8011,10303,19531,
%T A062700 17293,28057,30941,30103,131071,88741,86143,147073,524287,292561,
%U A062700 459007,492103,797161,552793,579883,598303,684757,704761,732541,735307
%N A062700 Terms of A000203 that are prime.
%C A062700 Sorted and duplicates removed, this gives A023195.
%H A062700 Harry J. Smith and Chai Wah Wu, <a href="/A062700/b062700.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..100 from Harry J. Smith)
%F A062700 a(n) = A000203(A023194(n)). - _Michel Marcus_, Oct 19 2019
%e A062700 sigma(2) = 3, sigma(4) = 7, sigma(9) = 13 are the first three prime terms of A000203. Hence the sequence starts 3, 7, 13.
%t A062700 Select[DivisorSigma[1,Range[1000000]],PrimeQ] (* _Harvey P. Dale_, Nov 09 2012 *)
%o A062700 (Magma) [ c: n in [1..1000000] | IsPrime(c) where c:=SumOfDivisors(n) ]; // _Klaus Brockhaus_, Oct 21 2009
%o A062700 (PARI) je=[]; for(n=1,1000000, if(isprime(sigma(n)),je=concat(je, sigma(n)))); je
%o A062700 (PARI) { n=0; for (m=1, 10^9, if(isprime(a=sigma(m)), write("b062700.txt", n++, " ", a); if (n==100, break)) ) } \\ _Harry J. Smith_, Aug 09 2009
%o A062700 (Python)
%o A062700 from sympy import isprime, divisor_sigma
%o A062700 A062700_list = [3]+[n for n in (divisor_sigma(d**2) for d in range(1,10**4)) if isprime(n)] # _Chai Wah Wu_, Jul 23 2016
%Y A062700 Cf. A000203 (sigma(n), sum of divisors of n), A023194, A034885 (record values of sigma(n)), A023195 (prime numbers that are the sum of the divisors of some n), A100382 (record values of A062700).
%K A062700 nonn
%O A062700 1,1
%A A062700 _Jason Earls_, Jul 11 2001
%E A062700 Edited by _Klaus Brockhaus_, Oct 21 2009