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

1,1

Comments

Sorted and duplicates removed, this gives A023195.

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

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).

Sequence in context: A109291 A340067 A199218 * A330835 A249378 A136060

Adjacent sequences: A062697 A062698 A062699 * A062701 A062702 A062703

Keyword

nonn

Author

Jason Earls, Jul 11 2001

Extensions

Edited by Klaus Brockhaus, Oct 21 2009

Status

approved