A359015 a(n) is the index of the smallest n-gonal pyramidal number with exactly n distinct prime factors.

7, 17, 84, 115, 220, 468, 3058, 5719, 18290, 182104, 144738, 1984619, 12051935, 41133455, 79156454

Offset: 3

Author

Ilya Gutkovskiy, Dec 12 2022

Keywords

• nonn
• more

Links

• Eric Weisstein's World of Mathematics, Distinct Prime Factors.
• Eric Weisstein's World of Mathematics, Pyramidal Number.

Crossrefs

Cf. A358864, A359016.

Programs

Mathematica

p[k_, n_] := k*(k + 1)*((n - 2)*k + 5 - n)/6; a[n_] := Module[{k = 1}, While[PrimeNu[p[k, n]] != n, k++]; k]; Array[a, 11, 3] (* Amiram Eldar, Jul 03 2025 *)

PARI

p(k, n) = k*(k + 1)*((n - 2)*k + 5 - n)/6;
a(n) = {my(k = 1); while(omega(p(k, n)) != n, k++); k;} \\ Amiram Eldar, Jul 03 2025

Extensions

a(16)-a(17) from Amiram Eldar, Jul 03 2025