A331188 Primorial inflation of A052126(n), where A052126(n) = n/(largest prime dividing n).

1, 1, 1, 2, 1, 2, 1, 4, 6, 2, 1, 4, 1, 2, 6, 8, 1, 12, 1, 4, 6, 2, 1, 8, 30, 2, 36, 4, 1, 12, 1, 16, 6, 2, 30, 24, 1, 2, 6, 8, 1, 12, 1, 4, 36, 2, 1, 16, 210, 60, 6, 4, 1, 72, 30, 8, 6, 2, 1, 24, 1, 2, 36, 32, 30, 12, 1, 4, 6, 60, 1, 48, 1, 2, 180, 4, 210, 12, 1, 16, 216, 2, 1, 24, 30, 2, 6, 8, 1, 72, 210, 4, 6, 2, 30, 32

Offset: 1

Author

Antti Karttunen, Jan 14 2020

Keywords

• nonn

Comments

The primorial inflation of n, A108951(n), divided by its largest squarefree divisor, which is also its largest primorial divisor.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A003557, A052126, A108951, A111701, A117366, A329348, A329382, A331292, A331293.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
A331188(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, A002110(primepi(f[i, 1]))^(f[i, 2]-(#f~==i))));

Formula

a(n) = A108951(A052126(n)).

a(n) = A003557(A108951(n)).

a(n) = A111701(A108951(n)) = A108951(n) / A002110(A061395(n)).

Other identities. For all >= 1:

A000005(a(n)) = A329382(n) = A005361(A108951(n)).

a(n) mod A117366(n) = A329348(n).