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

3,1

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, ...

Links

Table of n, a(n) for n=3..26.

Eric Weisstein's World of Mathematics, Prime Factor

Eric Weisstein's World of Mathematics, Pyramidal Number

Example

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.

Prog

(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

Crossrefs

Cf. A001222, A358862, A358863, A358864.

Sequence in context: A264308 A328174 A236988 * A134382 A105939 A054389

Adjacent sequences: A358862 A358863 A358864 * A358866 A358867 A358868

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 03 2022

Extensions

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

Status

approved