A086568 Smallest number having as many distinct prime factors as n has prime factors, when counted with multiplicity.

1, 2, 2, 6, 2, 6, 2, 30, 6, 6, 2, 30, 2, 6, 6, 210, 2, 30, 2, 30, 6, 6, 2, 210, 6, 6, 30, 30, 2, 30, 2, 2310, 6, 6, 6, 210, 2, 6, 6, 210, 2, 30, 2, 30, 30, 6, 2, 2310, 6, 30, 6, 30, 2, 210, 6, 210, 6, 6, 2, 210, 2, 6, 30, 30030, 6, 30, 2, 30, 6, 30, 2, 2310, 2, 6, 30, 30, 6, 30, 2

Offset: 1

Author

Reinhard Zumkeller, Jan 03 2004

Keywords

• nonn

Comments

a(n) = n if and only if n = A002110(m) for some m. That is, primorials give the fixed points of this sequence.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2310
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A001221, A001222, A002110, A130675, A292586.

Programs

Mathematica

Array[Times @@ Prime@ Range@ PrimeOmega@ # &, 79] (* Michael De Vlieger, Sep 25 2017 *)

PARI

A002110(n) = prod(i=1,n,prime(i));
A086568(n) = A002110(bigomega(n)); \\ Antti Karttunen, Jul 07 2017

Formula

a(n) = prime(bigomega(n))# = A002110(A001222(n)).

For all n >= 1, A001221(a(n)) = A001222(a(n)) = A001222(n).

Extensions

Formula corrected and comments edited by Antti Karttunen, Jul 07 2017