A076551 Smallest triangular number with n prime factors (counted without multiplicity).

1, 3, 6, 66, 210, 3570, 103740, 930930, 56812470, 1722580860, 32395433070, 265257422430, 91348974206490, 8923863379851420, 330196858581850260, 14193386885746698630, 2378522762792139793830, 351206814022419685159830, 28791787439593010836313310

Offset: 0

Author

Shyam Sunder Gupta, Oct 19 2002

Keywords

• nonn

Comments

a(19) <= 8285055066500101241048306610. a(20) <= 120052594044654305809137933570. - Donovan Johnson, Feb 28 2012

Examples

			a(0) = 1 because 1 is a triangular number with zero prime factors; a(3) = 66 because 66 = 2*3*11 is a triangular number with 3 distinct prime factors.
		

Crossrefs

Cf. A000217, A127637.

Programs

PARI

{n=12; v=vector(n); for(k=1,1000000,t=k*(k+1)/2; d=1+omega(t); if(d<=n&&v[d]<1,v[d]=t)); for(j=1,n,print1(v[j],","))}

Extensions

a(12) from Rick L. Shepherd, May 31 2003

a(13) from Klaus Brockhaus, Aug 02 2006

a(14)-a(16) from Donovan Johnson, Jan 28 2009

a(17) from Donovan Johnson, Feb 07 2009

a(18) from Donovan Johnson, Feb 28 2012