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.
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[ # ]][[2]]=={1, 1, 1}&]
Select[Accumulate[Range[200]], PrimeNu[#]==PrimeOmega[#]==3&] (* Harvey P. Dale, Apr 23 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Apr 20 2007
EXTENSIONS
Name clarified by Tanya Khovanova, Sep 06 2022
STATUS
approved