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%I #12 Sep 08 2022 08:45:38
%S 3,6,15,91,276,703,1431,1770,1891,2701,3486,4005,5356,8646,9730,11175,
%T 11476,12403,18721,19503,24976,25878,27261,28680,38503,43071,47278,
%U 49141,60378,61075,64620,72010,75855,79003,88831,98346,104653,106491
%N Triangular numbers p*(p+1)/2 with p prime such that 1+(number of prime factors of p+1) is prime.
%C Triangular numbers n(n+1)/2 such that n and A073093(n+1) are both prime.
%H Amiram Eldar, <a href="/A144549/b144549.txt">Table of n, a(n) for n = 1..10000</a>
%e 3 has one prime factor; 1+1 = 2 is prime, hence 2*3/2 = 3 is in the sequence.
%e 14 = 2*7 has two prime factors; 1+2 = 3 is prime, hence 13*14/2 = 91 is in the sequence.
%e 24 = 2*2*2*3 has four prime factors; 1+4 = 5 is prime, hence 23*24/2 = 276 is in the sequence.
%t aQ[n_] := PrimeQ[n] && PrimeQ[PrimeOmega[n + 1] + 1]; p = Select[Range[470], aQ]; p*(p + 1)/2 (* _Amiram Eldar_, Aug 31 2019 *)
%o (Magma) [ p*(p+1)/2: p in PrimesUpTo(490) | IsPrime(1 + &+[ f[2]: f in Factorization(p+1) ]) ];
%Y Cf. A000217 (triangular numbers), A000040 (prime numbers), A001222 (number of prime divisors of n), A073093.
%Y Subsequence of A034953. - _R. J. Mathar_, Jan 03 2009
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Dec 31 2008
%E Edited, corrected (3 inserted) and extended beyond a(16) by _Klaus Brockhaus_, Jan 05 2009
%E 3 inserted and extended by _R. J. Mathar_, Jan 03 2009
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