OFFSET
1,1
COMMENTS
All terms, usually ending with 7, give rise to odd abundant numbers (A005231). The first five terms that do not end with 7 are 111919, 121621, 391891, 480343, and 724531. Most terms are equal 1 mod 6, including all among the first 10^8 primes. Exceptions to this rule, as pointed out by Robert Israel, do exist.
A term not congruent to 1 mod 6 is 49079172691436387. - Robert Israel, Jan 18 2016
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
For n = 1, 2 * 787 + 1 = 1575, which is the second odd abundant number (see A005231).
MAPLE
select(p -> isprime(p) and numtheory:-sigma(2*p+1) > 2*(2*p+1), [seq(i, i=3..50000, 2)]); # Robert Israel, Jan 18 2016
MATHEMATICA
Select[Prime[Range[10000]], (DivisorSigma[1, 2 * # + 1] > 2(2 * # + 1)) &]
PROG
(PARI) isok(n) = isprime(n) && (sigma(2*n+1) > 4*n+2); \\ Michel Marcus, Jan 15 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Waldemar Puszkarz, Jan 15 2016
STATUS
approved