

A128896


Triangular numbers with exactly three distinct prime factors.


5



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
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OFFSET

1,1


COMMENTS

Numbers with three distinct prime factors, and also three prime factors counted with multiplicity.  Harvey P. Dale, Apr 23 2017


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.


MATHEMATICA

Select[Table[n(n+1)/2, {n, 1, 210}], Transpose[FactorInteger[ # ]][[2]]=={1, 1, 1}&]
Select[Accumulate[Range[200]], 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


STATUS

approved



