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A359089 a(n) is the index of the smallest tetrahedral number with exactly n distinct prime factors.

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%I A359089 #15 Feb 16 2025 08:34:04
%S A359089 1,2,3,7,18,34,90,259,988,2583,5795,37960,101268,424268,3344614,
%T A359089 17168723,74282570,351200178,1082950218,5313193819,31439710664,
%U A359089 317760710839,1782400663483
%N A359089 a(n) is the index of the smallest tetrahedral number with exactly n distinct prime factors.
%H A359089 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>
%H A359089 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>
%t A359089 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 A359089 (PARI) t(n) = n*(n+1)*(n+2)/6; \\ A000292
%o A359089 a(n) = my(k=1); while (omega(t(k)) != n, k++); k; \\ _Michel Marcus_, Dec 19 2022
%Y A359089 Cf. A000292, A001221, A156329, A359017, A359090.
%K A359089 nonn,more
%O A359089 0,2
%A A359089 _Ilya Gutkovskiy_, Dec 16 2022