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A127637
Smallest squarefree triangular number with exactly n prime factors.
4
1, 3, 6, 66, 210, 3570, 207690, 930930, 56812470, 1803571770, 32395433070, 265257422430, 91348974206490, 24630635909489610, 438603767516904990, 14193386885746698630, 2378522762792139793830, 351206814022419685159830, 28791787439593010836313310
OFFSET
0,2
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
LINKS
EXAMPLE
a(12) = 91348974206490 = 2*3*5*7*11*13*17*19*29*37*67*131 = A000217(13516580).
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Jan 28 2007, Feb 03 2007
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
STATUS
approved