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A302156
a(n) = Product_{k=1..n} prime(k+1)^(n-k+1).
0
1, 3, 45, 4725, 5457375, 81942485625, 20916229168209375, 101440469450294396296875, 11315322731906749607393607890625, 36603333436941101463129791457625571484375, 3670591247252362378693685549273035871463800818359375, 13619248222892703567716797493618519282116254094632750020888671875
OFFSET
0,2
COMMENTS
a(n) is the smallest odd number with n distinct exponents in its prime factorization.
FORMULA
a(0) = 1; a(n) = A002110(n+1)*a(n-1)/2.
a(n) = A006939(n+1)/A000079(n+1).
EXAMPLE
+---+-------------------------------+
| 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 |
+---+-------------------------------+
MATHEMATICA
Table[Product[Prime[k + 1]^(n - k + 1), {k, 1, n}], {n, 0, 11}]
PROG
(PARI) a(n) = prod(k=1, n, prime(k+1)^(n-k+1)); \\ Altug Alkan, Apr 02 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Apr 02 2018
STATUS
approved