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

0,2

Comments

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

Links

Table of n, a(n) for n=0..18.

Example

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.

Prog

(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], ", "))}

Crossrefs

Cf. A000217, A127637.

Sequence in context: A069077 A214838 A225789 * A127637 A306451 A068665

Adjacent sequences: A076548 A076549 A076550 * A076552 A076553 A076554

Keyword

nonn

Author

Shyam Sunder Gupta, Oct 19 2002

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

Status

approved