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

0,2

Links

Table of n, a(n) for n=0..22.

Eric Weisstein's World of Mathematics, Distinct Prime Factors

Eric Weisstein's World of Mathematics, Tetrahedral Number

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A058334 A303090 A131093 * A343358 A002864 A005248

Adjacent sequences: A359086 A359087 A359088 * A359090 A359091 A359092

Keyword

nonn,more

Author

Ilya Gutkovskiy, Dec 16 2022

Status

approved