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

0,2

Links

Table of n, a(n) for n=0..25.

Eric Weisstein's World of Mathematics, Prime Factor

Eric Weisstein's World of Mathematics, Square Pyramidal Number

Example

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.

Prog

(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

Crossrefs

Cf. A000330, A001222, A358927, A359193.

Sequence in context: A238604 A166068 A070129 * A359229 A081861 A372636

Adjacent sequences: A359189 A359190 A359191 * A359193 A359194 A359195

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 19 2022

Status

approved