A358929 a(n) is the smallest centered triangular number with exactly n prime factors (counted with multiplicity).

1, 19, 4, 316, 136, 760, 64, 4960, 22144, 103360, 27136, 5492224, 1186816, 41414656, 271212544, 559980544, 1334788096, 12943360, 7032930304, 527049293824, 158186536960, 1096295120896, 7871801589760, 154690378792960, 13071965224960, 56262393856, 964655941943296

Offset: 0

Author

Ilya Gutkovskiy, Dec 06 2022

Keywords

• nonn

Examples

			a(4) = 136, because 136 is a centered triangular number with 4 prime factors (counted with multiplicity) {2, 2, 2, 17} and this is the smallest such number.
		

Links

• Eric Weisstein's World of Mathematics, Centered Triangular Number
• Eric Weisstein's World of Mathematics, Prime Factor

Crossrefs

Cf. A001222, A005448, A075088, A358926, A358927, A358928.

Programs

Mathematica

c[k_] := (3*k^2 + 3*k + 2)/2; a[n_] := Module[{k = 0, ck}, While[PrimeOmega[ck = c[k]] != n, k++]; ck]; Array[a, 18, 0] (* Amiram Eldar, Dec 09 2022 *)

PARI

a(n) = if(n==0, return(1)); for(k=1, oo, my(t=3*k*(k+1)/2 + 1); if(bigomega(t) == n, return(t))); \\ Daniel Suteu, Dec 10 2022

Extensions

a(22)-a(26) from Daniel Suteu, Dec 10 2022