cp's OEIS Frontend

A075875 Triangular numbers that are 3-almost primes.

%I A075875 #21 Mar 27 2024 21:24:14
%S A075875 28,45,66,78,105,153,171,190,231,325,406,435,465,561,595,741,861,903,
%T A075875 946,1378,1653,2211,2278,2485,3081,3655,3741,4371,4465,4753,5151,5253,
%U A075875 5995,6441,7021,7381,7503,8515,8911,9453,9591,10011,10153,10585,11026
%N A075875 Triangular numbers that are 3-almost primes.
%H A075875 Charles R Greathouse IV, <a href="/A075875/b075875.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%F A075875 q:= n-> is(numtheory[bigomega](n)=3):
%F A075875 select(q, [i*(i+1)/2$i=0..200])[];  # _Alois P. Heinz_, Mar 27 2024
%e A075875 a(1)=28, 28 is a triangular number and 28 = 2*2*7, i.e., is a product of 3 prime factors so is 3-almost prime.
%t A075875 Select[Accumulate[Range[200]],PrimeOmega[#]==3&] (* _Harvey P. Dale_, Jul 24 2012 *)
%o A075875 (PARI) issemi(n)=bigomega(n)==2
%o A075875 ok(m,n)=if(isprime(m), issemi(n), isprime(n) && issemi(m))
%o A075875 list(lim)=my(v=List()); lim\=1; for(n=7,(sqrt(8*lim+1)-1)\2, if(if(n%2, ok(n,(n+1)/2), ok(n/2,n+1)), listput(v, n*(n+1)/2))); Vec(v) \\ _Charles R Greathouse IV_, Jun 12 2017
%Y A075875 Cf. A000217, A014612, A068443, A128896 (subsequence).
%K A075875 easy,nice,nonn
%O A075875 1,1
%A A075875 _Shyam Sunder Gupta_, Oct 19 2002