A249763 Numbers k such that sigma(k) + 2 is prime.

1, 2, 8, 18, 49, 72, 98, 128, 196, 200, 242, 288, 361, 392, 441, 676, 968, 1369, 1521, 1568, 1764, 1800, 2178, 2401, 2450, 2888, 3200, 3362, 3528, 3969, 4232, 5000, 5476, 5776, 5929, 6241, 6272, 7056, 7200, 7442, 7688, 7938, 8281, 8450, 8649, 9025, 9522, 9604

Offset

1,2

Comments

Except for 2, subsequence of nonprime numbers (A018252).

All odd terms are squares. - Michel Marcus, Dec 09 2014

Each term is either a square or twice a square. - Robert Israel, Dec 09 2014

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

8 is in the sequence because sigma(8)+2 = 15+2 = 17 (prime).

Maple

N:= 10^5: # to get all terms <= N
select(n -> isprime(numtheory:-sigma(n)+2), {seq(i^2, i=1..floor(sqrt(N))), seq(2*i^2, i=1..floor(sqrt(N/2)))} );
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(%, list)); # Robert Israel, Dec 09 2014

Mathematica

Select[Range[10000], PrimeQ[DivisorSigma[1, #] + 2] &] (* Vincenzo Librandi, Nov 14 2014 *)

Prog

(Magma) [n: n in[1..100000] | IsPrime(SumOfDivisors(n) + 2)]
(PARI) for(n=1, 10^5, if(isprime(sigma(n)+2), print1(n, ", "))) \\ Derek Orr, Nov 13 2014

Crossrefs

Cf. A000040, A000203, A018252.

Sequence in context: A201348 A102713 A332217 * A114723 A267638 A153335

Adjacent sequences: A249760 A249761 A249762 * A249764 A249765 A249766

Keyword

nonn,easy

Author

Jaroslav Krizek, Nov 13 2014

Status

approved