A075875 Triangular numbers that are 3-almost primes.

28, 45, 66, 78, 105, 153, 171, 190, 231, 325, 406, 435, 465, 561, 595, 741, 861, 903, 946, 1378, 1653, 2211, 2278, 2485, 3081, 3655, 3741, 4371, 4465, 4753, 5151, 5253, 5995, 6441, 7021, 7381, 7503, 8515, 8911, 9453, 9591, 10011, 10153, 10585, 11026

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Formula

q:= n-> is(numtheory[bigomega](n)=3):

select(q, [i*(i+1)/2$i=0..200])[]; # Alois P. Heinz, Mar 27 2024

Example

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.

Mathematica

Select[Accumulate[Range[200]], PrimeOmega[#]==3&] (* Harvey P. Dale, Jul 24 2012 *)

Prog

(PARI) issemi(n)=bigomega(n)==2
ok(m, n)=if(isprime(m), issemi(n), isprime(n) && issemi(m))
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

Crossrefs

Cf. A000217, A014612, A068443, A128896 (subsequence).

Sequence in context: A219685 A180045 A144581 * A332764 A116541 A292989

Adjacent sequences: A075872 A075873 A075874 * A075876 A075877 A075878

Keyword

easy,nice,nonn

Author

Shyam Sunder Gupta, Oct 19 2002

Status

approved