A127637 Smallest squarefree triangular number with exactly n prime factors.

1, 3, 6, 66, 210, 3570, 207690, 930930, 56812470, 1803571770, 32395433070, 265257422430, 91348974206490, 24630635909489610, 438603767516904990, 14193386885746698630, 2378522762792139793830, 351206814022419685159830, 28791787439593010836313310

Offset: 0

Author

Rick L. Shepherd, Jan 28 2007, Feb 03 2007

Keywords

• nonn

Comments

The sequence of smallest squarefree triangular numbers with at least n prime factors has identical terms through 91348974206490 at least.

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

Examples

			a(12) = 91348974206490 = 2*3*5*7*11*13*17*19*29*37*67*131 = A000217(13516580).
		

Links

• Daniel Suteu, Table of n, a(n) for n = 0..21

Crossrefs

Cf. A075088, A076551, A005117, A000217.

Programs

PARI

squarefree_omega_polygonals(A, B, n, k) = A=max(A, vecprod(primes(n))); (f(m, p, j) = my(list=List()); my(s=sqrtnint(B\m, j)); if(j==1, forprime(q=max(p, ceil(A/m)), s, if(ispolygonal(m*q, k), listput(list, m*q))), forprime(q=p, s, my(t=m*q); list=concat(list, f(t, q+1, j-1)))); list); vecsort(Vec(f(1, 2, n)));
a(n, k=3) = if(n==0, return(1)); my(x=vecprod(primes(n)), y=2*x); while(1, my(v=squarefree_omega_polygonals(x, y, n, k)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ Daniel Suteu, Jan 18 2023

Extensions

a(13)-a(16) from Donovan Johnson, Jan 28 2009

a(17) from Donovan Johnson, Feb 07 2009

a(18) from Donovan Johnson, Feb 28 2012