A162409 Semiprimes of the form p*(k*p-1) where k > 1 (and p prime).

6, 10, 14, 15, 22, 26, 33, 34, 38, 46, 51, 58, 62, 69, 74, 82, 86, 87, 91, 94, 95, 106, 118, 122, 123, 134, 141, 142, 145, 146, 158, 159, 166, 177, 178, 194, 202, 206, 213, 214, 218, 226, 249, 254, 262, 267, 274, 278, 287, 295, 298, 302, 303, 314, 321, 326, 334

Offset: 1

Author

Vassilis Papadimitriou, Jul 02 2009

Keywords

• nonn

Comments

Regarding k = 1: 3 is the only prime p such that p-1 is prime, so 3*(1*3-1) = 6. But 6 is a term for p = 2 and k = 2 (see example), therefore the sequence does not change if k = 1 is allowed in the definition.

Examples

			For p = 2 and k = 2 we have 2*(2*2-1) = 6, so 6 is a term. For p = 3 and k = 6 we have 3*(6*3-1) = 51, so 51 is a term.
		

Crossrefs

Subsequence of A006881 (product of two distinct primes).

Programs

Magma

m:=170; { s: p, q in PrimesUpTo(m) | s le 2*m and exists(t){ k: k in [2..p*q div 2] | q eq p*k-1 } where s is p*q };

Extensions

Edited, corrected and extended by Klaus Brockhaus, Jul 06 2009