A359089 a(n) is the index of the smallest tetrahedral number with exactly n distinct prime factors.
1, 2, 3, 7, 18, 34, 90, 259, 988, 2583, 5795, 37960, 101268, 424268, 3344614, 17168723, 74282570, 351200178, 1082950218, 5313193819, 31439710664, 317760710839, 1782400663483
Offset: 0
Links
- Eric Weisstein's World of Mathematics, Distinct Prime Factors
- Eric Weisstein's World of Mathematics, Tetrahedral Number
Programs
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Mathematica
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 *) -
PARI
t(n) = n*(n+1)*(n+2)/6; \\ A000292 a(n) = my(k=1); while (omega(t(k)) != n, k++); k; \\ Michel Marcus, Dec 19 2022