A267476 Primes p such that 2*p + 1 is abundant.

787, 2677, 2887, 3217, 3307, 4567, 5197, 5827, 7507, 7717, 9817, 10867, 11497, 12757, 12967, 14107, 14437, 15277, 15907, 16087, 16747, 17077, 18427, 19687, 20947, 21157, 23017, 23677, 23887, 24097, 25357, 28297, 29137, 29347, 31237, 31657, 32077, 32917, 33547, 33637, 34807, 35227, 35437, 37537, 39217

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

Cf. A000040 (prime numbers), A005231 (odd abundant numbers).

Sequence in context: A097774 A031896 A045231 * A068660 A097775 A321210

Adjacent sequences: A267473 A267474 A267475 * A267477 A267478 A267479

Keyword

nonn

Author

Waldemar Puszkarz, Jan 15 2016

Status

approved