A070043 Numbers of the form 6*j*k+j+k for positive integers j and k.

8, 15, 22, 28, 29, 36, 41, 43, 50, 54, 57, 60, 64, 67, 71, 78, 79, 80, 85, 92, 93, 98, 99, 104, 106, 113, 117, 119, 120, 127, 129, 132, 134, 136, 141, 145, 148, 154, 155, 158, 160, 162, 169, 171, 174, 176, 179, 183, 184, 190, 191, 193, 197, 204, 210, 211, 212

Offset: 1

Author

Jon Perry, May 05 2002

Keywords

• nonn

Comments

Equivalently, numbers r such that 6*r+1 has a nontrivial factor == 1 (mod 6).

These numbers, together with numbers of the form 6*j*k-j-k (A070799) are the numbers s for which 6*s+1 is composite (A046954). If we also add in the numbers of the form 6*j*k+j-k (A046953), we get the numbers t such that 6*t-1 and 6*t+1 do not form a pair of twin primes (A067611).

If N is the set of natural numbers, then the set N-{A070043 U A070799} are the numbers k that make 6*k+1 prime. - Pedro Caceres, Jan 22 2018

Examples

			41 = 6*2*3 + 2 + 3. Equivalently, 6*41+1 = (6*2+1)*(6*3+1).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..9000

Crossrefs

Cf. A070799, A046953, A046954, A067611.

Programs

Mathematica

Select[Range[250], MemberQ[Mod[Take[Divisors[6#+1], {2, -2}], 6], 1]&]

Extensions

Edited by Dean Hickerson and Vladeta Jovovic, May 07 2002