A292586 a(n) = A002110(A001221(n)) = product of first omega(n) primes.

1, 2, 2, 2, 2, 6, 2, 2, 2, 6, 2, 6, 2, 6, 6, 2, 2, 6, 2, 6, 6, 6, 2, 6, 2, 6, 2, 6, 2, 30, 2, 2, 6, 6, 6, 6, 2, 6, 6, 6, 2, 30, 2, 6, 6, 6, 2, 6, 2, 6, 6, 6, 2, 6, 6, 6, 6, 6, 2, 30, 2, 6, 6, 2, 6, 30, 2, 6, 6, 30, 2, 6, 2, 6, 6, 6, 6, 30, 2, 6, 2, 6, 2, 30, 6, 6, 6, 6, 2, 30, 6, 6, 6, 6, 6, 6, 2, 6, 6, 6, 2, 30, 2, 6, 30

Offset: 1

Author

Antti Karttunen, Sep 25 2017

Keywords

• nonn

Comments

The connection with binary tree A005940 is explained by the fact that on a trajectory from its root (1) to any number n, the numbers of the form 4k+2 will never occur consecutively (they are only born as right children of odd numbers, while all their right descendants from then onward are multiples of four). Thus all the runs are separate runs of length one, from which follows that A278222 when applied to A292382 yields only primorials. Moreover, the steps producing 4k+2 numbers are also only steps in A005940 that add new distinct prime factors to the generated number. Thus the total number of such steps is equal to the number of distinct prime factors of the eventual n. Hence A278222(A292382(n)) = A002110(A001221(n)).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A005940, A086568, A278222, A292382.

Cf. A083399 (restricted growth transform of this sequence).

Programs

Mathematica

Array[Product[Prime@ i, {i, PrimeNu@ #}] &, 105] (* Michael De Vlieger, Sep 25 2017 *)

PARI

A292586(n) = prod(i=1, omega(n), prime(i));

Scheme

(define (A292586 n) (A002110 (A001221 n)))
(define (A292586 n) (A278222 (A292382 n)))

Formula

a(n) = A002110(A001221(n)).

a(n) = A278222(A292382(n)).

For all n >= 1:

A001221(n) = A001221(a(n)) = A001222(a(n)) = A000120(A292382(n)).