OFFSET
0,2
COMMENTS
a(n) cannot be divisible by a bunch of primes like 3, 7, 11, 13, ... as (3*k^2 + 3*k + 2)/2 is never a multiple of any of them. - David A. Corneth, Dec 12 2022
a(16) <= 1421044357661885128003268103460. - David A. Corneth, Dec 14 2022
LINKS
Eric Weisstein's World of Mathematics, Centered Triangular Number
Eric Weisstein's World of Mathematics, Distinct Prime Factors
EXAMPLE
a(4) = 9010, because 9010 is a centered triangular number with 4 distinct prime factors {2, 5, 17, 53} and this is the smallest such number.
MATHEMATICA
c[k_] := (3*k^2 + 3*k + 2)/2; a[n_] := Module[{k = 0, ck}, While[PrimeNu[ck = c[k]] != n, k++]; ck]; Array[a, 9, 0] (* Amiram Eldar, Dec 09 2022 *)
PROG
(PARI) a(n) = for(k=0, oo, my(t=3*k*(k+1)/2 + 1); if(omega(t) == n, return(t))); \\ Daniel Suteu, Dec 10 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 06 2022
EXTENSIONS
a(9)-a(11) from Daniel Suteu, Dec 10 2022
a(12)-a(13) from David A. Corneth, Dec 12 2022
a(13) corrected by Daniel Suteu, Dec 13 2022
a(14)-a(15) from David A. Corneth, Dec 14 2022
a(16) from Daniel Suteu, Dec 14 2022
a(15) corrected by Daniel Suteu, Dec 15 2022
STATUS
approved