A359192 a(n) is the smallest square pyramidal number with exactly n prime factors (counted with multiplicity).

1, 5, 14, 30, 140, 1240, 4900, 10416, 85344, 173880, 1801800, 5559680, 44608256, 357389824, 44870400, 110099203200, 2861214720, 98269966080, 982218617856, 1466149724160, 11727587164160, 243912389529600, 750591347982336, 1951282875801600, 37635982963937280, 460962807482777600

Offset: 0

Author

Ilya Gutkovskiy, Dec 19 2022

Keywords

• nonn

Examples

			a(4) = 140, because 140 is a square pyramidal number with 4 prime factors (counted with multiplicity) {2, 2, 5, 7} and this is the smallest such number.
		

Links

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

Crossrefs

Cf. A000330, A001222, A358927, A359193.

Programs

PARI

sp(n) = n*(n+1)*(2*n+1)/6; \\ A000330
a(n) = my(k=1); while (bigomega(sp(k)) != n, k++); sp(k); \\ Michel Marcus, Dec 20 2022