A181555 - OEIS

A181555

a(n) = A002110(n)^n.

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

(list; graph; refs; listen; history; text; internal format)

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.

Every natural number divides sufficiently large terms of this sequence. In particular, k divides a(A263323(k)) and all subsequent terms. - Hal M. Switkay, Mar 06 2026

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 (n-k) 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: A127234 A326961 A397599 * A306644 A283261 A280420

Adjacent sequences: A181552 A181553 A181554 * A181556 A181557 A181558

KEYWORD

easy,nonn

AUTHOR

Matthew Vandermast, Oct 31 2010

STATUS

approved