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A075875
Triangular numbers that are 3-almost primes.
6
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
KEYWORD
easy,nice,nonn
AUTHOR
Shyam Sunder Gupta, Oct 19 2002
STATUS
approved