A302156 a(n) = Product_{k=1..n} prime(k+1)^(n-k+1).

1, 3, 45, 4725, 5457375, 81942485625, 20916229168209375, 101440469450294396296875, 11315322731906749607393607890625, 36603333436941101463129791457625571484375, 3670591247252362378693685549273035871463800818359375, 13619248222892703567716797493618519282116254094632750020888671875

Offset: 0

Author

Ilya Gutkovskiy, Apr 02 2018

Keywords

• nonn
• easy

Comments

a(n) is the smallest odd number with n distinct exponents in its prime factorization.

Examples

			+---+-------------------------------+
| n |  prime factorization of a(n)  |
+---+-------------------------------+
| 1 | 3                             |
| 2 | 3^2*5                         |
| 3 | 3^3*5^2*7                     |
| 4 | 3^4*5^3*7^2*11                |
| 5 | 3^5*5^4*7^3*11^2*13           |
| 6 | 3^6*5^5*7^4*11^3*13^2*17      |
| 7 | 3^7*5^6*7^5*11^4*13^3*17^2*19 |
+---+-------------------------------+
		

Crossrefs

Cf. A000079, A002110, A006939, A070826, A076954, A087315.

Programs

Mathematica

Table[Product[Prime[k + 1]^(n - k + 1), {k, 1, n}], {n, 0, 11}]

PARI

a(n) = prod(k=1, n, prime(k+1)^(n-k+1)); \\ Altug Alkan, Apr 02 2018

Formula

a(0) = 1; a(n) = A002110(n+1)*a(n-1)/2.

a(n) = A006939(n+1)/A000079(n+1).