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A062700
Terms of A000203 that are prime.
19
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
KEYWORD
nonn
AUTHOR
Jason Earls, Jul 11 2001
EXTENSIONS
Edited by Klaus Brockhaus, Oct 21 2009
STATUS
approved