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A128896 Triangular numbers with exactly three distinct prime factors. 2
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

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: A039538 A095751 A121478 * A109750 A127654 A032485

Adjacent sequences:  A128893 A128894 A128895 * A128897 A128898 A128899

KEYWORD

nonn

AUTHOR

Zak Seidov, Apr 20 2007

STATUS

approved

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Last modified October 17 10:50 EDT 2017. Contains 293469 sequences.