login
A331188
Primorial inflation of A052126(n), where A052126(n) = n/(largest prime dividing n).
9
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
1,4
COMMENTS
The primorial inflation of n, A108951(n), divided by its largest squarefree divisor, which is also its largest primorial divisor.
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).
PROG
(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))));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 14 2020
STATUS
approved