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

1,2

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

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A187223 A349921 A175194 * A351091 A239074 A160122

Adjacent sequences: A086565 A086566 A086567 * A086569 A086570 A086571

Keyword

nonn

Author

Reinhard Zumkeller, Jan 03 2004

Extensions

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

Status

approved