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 A128896 Triangular numbers that are products of three distinct primes. 8
 66, 78, 105, 190, 231, 406, 435, 465, 561, 595, 741, 861, 903, 946, 1378, 1653, 2211, 2278, 2485, 3081, 3655, 3741, 4371, 4465, 5151, 5253, 5995, 6441, 7021, 7503, 8515, 8911, 9453, 9591, 10011, 10153, 10585, 11026, 12561, 13366, 14878, 15051, 15753 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 FORMULA a(n) = T(k) = k*(k+1)/2 = p*q*r for some k,p,q,r, where T(k) is triangular number and p, q, r are distinct primes. Equals A000217 INTERSECT A007304 and A075875 INTERSECT A121478. - R. J. Mathar, Apr 22 2007 EXAMPLE a(1)=T(11)=66=2*3*11, a(2)=T(12)=78=2*3*13, a(3)=T(14)=105=3*5*7, a(4)=T(19)=190=2*5*19, a(5)=T(21)=231=3*7*11, a(6)=T(28)=406=2*7*29. T(15) = 120 = 2^3*3*5. The triangular 120 has three prime factors but is not a product of these factors. Thus, 120 is not in this sequence. MATHEMATICA Select[Table[n(n+1)/2, {n, 1, 210}], Transpose[FactorInteger[ # ]][]=={1, 1, 1}&] Select[Accumulate[Range], PrimeNu[#]==PrimeOmega[#]==3&] (* Harvey P. Dale, Apr 23 2017 *) CROSSREFS Cf. A000217, A068443, A069903, A076551, A127637. Sequence in context: A095751 A121478 A330809 * A109750 A127654 A293175 Adjacent sequences: A128893 A128894 A128895 * A128897 A128898 A128899 KEYWORD nonn AUTHOR Zak Seidov, Apr 20 2007 EXTENSIONS Name clarified by Tanya Khovanova, Sep 06 2022 STATUS approved

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Last modified March 23 19:26 EDT 2023. Contains 361449 sequences. (Running on oeis4.)