A358864 a(n) is the smallest n-gonal pyramidal number with exactly n distinct prime factors.

84, 1785, 299880, 1020510, 8897460, 102612510, 33367223274, 249417828660, 9177835927260, 10064864238489060, 5558913993302670, 15633689593760207970, 3792821921183752657200

Offset: 3

Author

Ilya Gutkovskiy, Dec 03 2022

Keywords

• nonn
• more

Comments

The corresponding indices of n-gonal pyramidal numbers are 7, 17, 84, 115, 220, 468, 3058, 5719, 18290, ...

Examples

			a(3) = 84, because 84 is a tetrahedral (or triangular pyramidal) number with 3 distinct prime factors {2, 3, 7} and this is the smallest such number.
		

Links

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

Crossrefs

Cf. A001221, A156329, A358862, A358863, A358865.

Programs

PARI

a(n) = if(n<3, return()); for(k=1, oo, my(t=(k*(k+1)*((n-2)*k + (5-n)))\6); if(omega(t) == n, return(t))); \\ Daniel Suteu, Dec 05 2022

Extensions

a(12)-a(15) from Daniel Suteu, Dec 05 2022