A062700 Terms of A000203 that are prime.

3, 7, 13, 31, 31, 127, 307, 1093, 1723, 2801, 3541, 8191, 5113, 8011, 10303, 19531, 17293, 28057, 30941, 30103, 131071, 88741, 86143, 147073, 524287, 292561, 459007, 492103, 797161, 552793, 579883, 598303, 684757, 704761, 732541, 735307

Offset: 1

Author

Jason Earls, Jul 11 2001

Keywords

• nonn

Comments

Sorted and duplicates removed, this gives A023195.

Examples

			sigma(2) = 3, sigma(4) = 7, sigma(9) = 13 are the first three prime terms of A000203. Hence the sequence starts 3, 7, 13.
		

Links

• Harry J. Smith and Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..100 from Harry J. Smith)

Crossrefs

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).

Programs

Magma

[ c: n in [1..1000000] | IsPrime(c) where c:=SumOfDivisors(n) ]; // Klaus Brockhaus, Oct 21 2009

Mathematica

Select[DivisorSigma[1,Range[1000000]],PrimeQ] (* Harvey P. Dale, Nov 09 2012 *)

PARI

je=[]; for(n=1,1000000, if(isprime(sigma(n)),je=concat(je, sigma(n)))); je

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

Python

from sympy import isprime, divisor_sigma
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

Formula

a(n) = A000203(A023194(n)). - Michel Marcus, Oct 19 2019

Extensions

Edited by Klaus Brockhaus, Oct 21 2009