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%I #9 Dec 11 2022 11:59:25
%S 1,19,4,316,136,760,64,4960,22144,103360,27136,5492224,1186816,
%T 41414656,271212544,559980544,1334788096,12943360,7032930304,
%U 527049293824,158186536960,1096295120896,7871801589760,154690378792960,13071965224960,56262393856,964655941943296
%N a(n) is the smallest centered triangular number with exactly n prime factors (counted with multiplicity).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CenteredTriangularNumber.html">Centered Triangular Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>
%e 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.
%t 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 *)
%o (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
%Y Cf. A001222, A005448, A075088, A358926, A358927, A358928.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Dec 06 2022
%E a(22)-a(26) from _Daniel Suteu_, Dec 10 2022