



1, 2, 36, 27000, 1944810000, 65774855015100000, 733384949590939374729000000, 9037114296609938214167920266348510000000, 78354300210436852307898467208663359164858967744100000000
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OFFSET

0,2


COMMENTS

For n>0, a(n)= first counting number whose prime signature consists of n repeated n times (cf. A002024). Subsequence of A025487.


LINKS

Amiram Eldar, Table of n, a(n) for n = 0..26


FORMULA

a(n) = A079474(2n,n).  Alois P. Heinz, Aug 22 2019


EXAMPLE

a(4) = 1944810000 = 210^4 = 2^4 * 3^4 * 5^4 * 7^4.


MATHEMATICA

a[0] = 1; a[n_] := Product[Prime[i], {i, 1, n}]^n; Array[a, 9, 0] (* Amiram Eldar, Aug 08 2019 *)


CROSSREFS

A061742(n) = A002110(n)^2. See also A006939, A066120, A166475, A167448.
A000005(a(n)) = A000169(n). The divisors of a(n) appear as the first A000169(n) terms of A178479, with A178479(A000169(n)) = a(n).
A071207(n, k) gives the number of divisors of n with (nk) distinct prime factors, A181567(n, k) gives the number of divisors of n with k prime factors counted with multiplicity.
Cf. A001221, A001222, A079474, A146290, A146292.
Sequence in context: A265944 A127234 A326961 * A306644 A283261 A280420
Adjacent sequences: A181552 A181553 A181554 * A181556 A181557 A181558


KEYWORD

easy,nonn


AUTHOR

Matthew Vandermast, Oct 31 2010


STATUS

approved



