

A037020


Numbers whose sum of proper (or aliquot) divisors is a prime.


19



4, 8, 21, 27, 32, 35, 39, 50, 55, 57, 63, 65, 77, 85, 98, 111, 115, 125, 128, 129, 155, 161, 171, 175, 185, 187, 189, 201, 203, 205, 209, 221, 235, 237, 242, 245, 265, 275, 279, 291, 299, 305, 309, 319, 323, 324, 325, 327, 335, 338, 341, 365, 371, 377, 381
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



FORMULA



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 !! (n1)
a037020_list = filter ((== 1) . a010051' . a001065) [1..]
(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



STATUS

approved



