A144549 Triangular numbers p*(p+1)/2 with p prime such that 1+(number of prime factors of p+1) is prime.

3, 6, 15, 91, 276, 703, 1431, 1770, 1891, 2701, 3486, 4005, 5356, 8646, 9730, 11175, 11476, 12403, 18721, 19503, 24976, 25878, 27261, 28680, 38503, 43071, 47278, 49141, 60378, 61075, 64620, 72010, 75855, 79003, 88831, 98346, 104653, 106491

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 31 2008

Keywords

• nonn

Comments

Triangular numbers n(n+1)/2 such that n and A073093(n+1) are both prime.

Examples

			3 has one prime factor; 1+1 = 2 is prime, hence 2*3/2 = 3 is in the sequence.
14 = 2*7 has two prime factors; 1+2 = 3 is prime, hence 13*14/2 = 91 is in the sequence.
24 = 2*2*2*3 has four prime factors; 1+4 = 5 is prime, hence 23*24/2 = 276 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217 (triangular numbers), A000040 (prime numbers), A001222 (number of prime divisors of n), A073093.

Subsequence of A034953. - R. J. Mathar, Jan 03 2009

Programs

Magma

[ p*(p+1)/2: p in PrimesUpTo(490) | IsPrime(1 + &+[ f[2]: f in Factorization(p+1) ]) ];

Mathematica

aQ[n_] := PrimeQ[n] && PrimeQ[PrimeOmega[n + 1] + 1]; p = Select[Range[470], aQ]; p*(p + 1)/2 (* Amiram Eldar, Aug 31 2019 *)

Extensions

Edited, corrected (3 inserted) and extended beyond a(16) by Klaus Brockhaus, Jan 05 2009

3 inserted and extended by R. J. Mathar, Jan 03 2009