A358865 a(n) is the smallest n-gonal pyramidal number with exactly n prime factors (counted with multiplicity).

20, 140, 405, 2856, 25296, 111720, 25984, 5474000, 237600, 223826688, 3852800, 268565760, 1834725376, 175861400000, 335674368, 2863363937280, 4383831556096, 206015846400, 3400704000, 938209120583680, 2981338216980480, 21463949229465600, 45410367307776, 72056803765911552

Offset: 3

Author

Ilya Gutkovskiy, Dec 03 2022

Keywords

• nonn

Comments

The corresponding indices of n-gonal pyramidal numbers are 4, 7, 9, 16, 31, 48, 28, 160, 54, 512, 128, 512, 946, 4224, 512, 10240, 11566, 4095, 1024, ...

Examples

			a(3) = 20, because 20 is a tetrahedral (or triangular pyramidal) number with 3 prime factors (counted with multiplicity) {2, 2, 5} and this is the smallest such number.
		

Links

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

Crossrefs

Cf. A001222, A358862, A358863, A358864.

Programs

PARI

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

Extensions

a(22)-a(26) from Daniel Suteu, Dec 05 2022