OFFSET
1,1
COMMENTS
Assuming the Goldbach conjecture, it is easy to show that all primes, except 2 and 5, are the sum of the proper divisors of some number. - T. D. Noe, Nov 29 2006
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
Paul Pollack, Some arithmetic properties of the sum of proper divisors and the sum of prime divisors, Illinois J. Math. 58:1 (2014), pp. 125-147.
FORMULA
Pollack proves that a(n) >> n log n. - Charles R Greathouse IV, Jun 28 2021
EXAMPLE
The aliquot divisors of 27 are 1, 3, and 9, whose sum is 13, a prime, so 27 is a term.
MATHEMATICA
Select[Range[400], PrimeQ[DivisorSigma[1, #]-#]&] (* Harvey P. Dale, May 09 2011 *)
PROG
(Haskell)
a037020 n = a037020_list !! (n-1)
a037020_list = filter ((== 1) . a010051' . a001065) [1..]
-- Reinhard Zumkeller, Nov 01 2015, Sep 15 2011
(PARI) isok(n) = isprime(sigma(n) - n); \\ Michel Marcus, Nov 01 2016
(Magma) [n: n in [2..500] | IsPrime(SumOfDivisors(n)-n)]; // Vincenzo Librandi, Nov 01 2016
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
Felice Russo, Dec 11 1999
STATUS
approved