A328613 Starting with m = 1, p = 2 and x = n, iterate m -> m * p^valuation(x,p), x -> floor(x/p), p -> {the next prime after p}, until x is zero. Then a(n) = product of the values of m and p that were reached at the end of the iteration.

2, 3, 10, 5, 20, 5, 42, 21, 56, 7, 14, 7, 84, 21, 14, 7, 112, 7, 126, 63, 28, 7, 14, 7, 168, 21, 14, 7, 28, 7, 330, 165, 1760, 55, 110, 55, 396, 99, 22, 11, 88, 11, 66, 33, 44, 11, 22, 11, 528, 33, 22, 11, 44, 11, 594, 297, 88, 11, 22, 11, 660, 165, 110, 55, 3520, 55, 66, 33, 44, 11, 22, 11, 792, 99, 22, 11, 44, 11, 66, 33, 176, 11

Offset: 0

Author

Antti Karttunen, Oct 22 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..32768
• Index entries for sequences related to primorial base

Crossrefs

Cf. A000040, A007814, A020639, A055396, A049345, A143293, A235224, A276086, A326810, A328570, A328612.

Programs

PARI

A328613(n) = { my(m=1, p=2); while(n, m *= p^valuation(n,p); n = n\p; p = nextprime(1+p)); (m*p); };

Formula

a(n) = A000040(1+A235224(n)) * A328612(n).

For all n >= 0, A055396(a(n)) = A328570(n) and A020639(a(n)) = A326810(n).

For all n >= 1, A007814(a(n)) = A007814(n).

For all n >= 1, a(A143293(n-1)) = A000040(1+n).