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%I #6 Dec 11 2022 11:57:02
%S 1,-1,4,20,56,120,560,4960,19600,41664,341376,695520,7207200,22238720,
%T 178433024,1429559296,179481600,11453245440,11444858880,393079864320,
%U 3928874471424,5864598896640,46910348656640,975649558118400,3002365391929344,7805131503206400
%N a(n) is the smallest tetrahedral number with exactly n prime factors (counted with multiplicity), or -1 if no such number exists.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>
%e a(4) = 56, because 56 is a tetrahedral number with 4 prime factors (counted with multiplicity) {2, 2, 2, 7} and this is the smallest such number.
%t t[k_] := k*(k + 1)*(k + 2)/6; a[n_] := Module[{k = 1, tk}, While[PrimeOmega[tk = t[k]] != n, k++]; tk]; a[1] = -1; Array[a, 26, 0] (* _Amiram Eldar_, Dec 09 2022 *)
%Y Cf. A000292, A001222, A075088, A156329, A279082, A358865.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Dec 06 2022