A244520 a(n) = A080715(n+1) / 2.

1, 3, 5, 11, 15, 21, 29, 35, 39, 41, 51, 65, 95, 105, 155, 165, 179, 191, 221, 231, 239, 281, 329, 371, 419, 431, 485, 519, 611, 641, 659, 809, 905, 935, 989, 1019, 1031, 1049, 1121, 1199, 1229, 1289, 1451, 1469, 1481, 1509, 1541, 1661, 1821, 1931, 2109, 2129, 2141, 2339, 2549, 2795, 2969, 3021, 3039, 3189, 3299, 3329

Offset: 1

Author

Joerg Arndt, Jul 10 2014

Keywords

• nonn

Comments

Numbers k such that 2d + k/d is prime for every d|k. Such k must be an odd squarefree number. Primes in the sequence are A045536. - Thomas Ordowski, Nov 16 2017

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A045536, A080715, A088627.

Programs

Mathematica

Select[Range[1, 3400, 2], Function[n, AllTrue[Divisors@ n, PrimeQ[2 # + n/#] &]]] (* Michael De Vlieger, Nov 18 2017 *)

PARI

is_ok(n)=n=2*n;fordiv(n,d,if(!isprime(d+n/d),return(0)));return(1);
for(n=1,10^4,if(is_ok(n),print1(n,", ")));

Formula

A088627(a(n)) = A000005(a(n)) = 2^m. - Thomas Ordowski, Nov 16 2017