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a(n) is the index of the smallest tetrahedral number with exactly n distinct prime factors.
1

%I #14 Dec 19 2022 17:28:59

%S 1,2,3,7,18,34,90,259,988,2583,5795,37960,101268,424268,3344614,

%T 17168723,74282570,351200178,1082950218,5313193819,31439710664,

%U 317760710839,1782400663483

%N a(n) is the index of the smallest tetrahedral number with exactly n distinct prime factors.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>

%t r = -1; Reap[Do[If[# > r, r = #; Sow[n]] &[PrimeNu[n (n + 1) (n + 2)/6]], {n, 2^19}] ][[-1, -1]] (* _Michael De Vlieger_, Dec 19 2022 *)

%o (PARI) t(n) = n*(n+1)*(n+2)/6; \\ A000292

%o a(n) = my(k=1); while (omega(t(k)) != n, k++); k; \\ _Michel Marcus_, Dec 19 2022

%Y Cf. A000292, A001221, A156329, A359017, A359090.

%K nonn,more

%O 0,2

%A _Ilya Gutkovskiy_, Dec 16 2022