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a(n) = Product_{k=1..n} prime(k+1)^(n-k+1).
0

%I #12 Apr 03 2018 15:11:32

%S 1,3,45,4725,5457375,81942485625,20916229168209375,

%T 101440469450294396296875,11315322731906749607393607890625,

%U 36603333436941101463129791457625571484375,3670591247252362378693685549273035871463800818359375,13619248222892703567716797493618519282116254094632750020888671875

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

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

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

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

%e +---+-------------------------------+

%e | n | prime factorization of a(n) |

%e +---+-------------------------------+

%e | 1 | 3 |

%e | 2 | 3^2*5 |

%e | 3 | 3^3*5^2*7 |

%e | 4 | 3^4*5^3*7^2*11 |

%e | 5 | 3^5*5^4*7^3*11^2*13 |

%e | 6 | 3^6*5^5*7^4*11^3*13^2*17 |

%e | 7 | 3^7*5^6*7^5*11^4*13^3*17^2*19 |

%e +---+-------------------------------+

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

%o (PARI) a(n) = prod(k=1, n, prime(k+1)^(n-k+1)); \\ _Altug Alkan_, Apr 02 2018

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

%K nonn,easy

%O 0,2

%A _Ilya Gutkovskiy_, Apr 02 2018