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A364255
a(n) = gcd(n, A163511(n)).
18
1, 1, 2, 3, 4, 1, 6, 1, 8, 9, 2, 1, 12, 1, 2, 1, 16, 1, 18, 1, 4, 3, 2, 1, 24, 5, 2, 1, 4, 1, 2, 1, 32, 3, 2, 5, 36, 1, 2, 1, 8, 1, 6, 1, 4, 3, 2, 1, 48, 1, 10, 1, 4, 1, 2, 11, 8, 3, 2, 1, 4, 1, 2, 1, 64, 1, 6, 1, 4, 3, 10, 1, 72, 1, 2, 5, 4, 7, 2, 1, 16, 27, 2, 1, 12, 5, 2, 1, 8, 1, 6, 1, 4, 3, 2, 1, 96, 1, 2, 1, 20, 1, 2, 1, 8, 105
OFFSET
0,3
FORMULA
From Antti Karttunen, Sep 01 2023: (Start)
a(n) = gcd(n, A364258(n)) = gcd(A163511(n), A364258(n)).
a(n) = n / A364491(n) = A163511(n)/ A364492(n).
(End)
PROG
(Python)
from math import gcd
from sympy import nextprime
def A364255(n):
c, p, k = 1, 1, n
while k:
c *= (p:=nextprime(p))**(s:=(~k&k-1).bit_length())
k >>= s+1
return gcd(c*p, n) # Chai Wah Wu, Jul 25 2023
(PARI)
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A364255(n) = gcd(n, A163511(n)); \\ Antti Karttunen, Sep 01 2023
CROSSREFS
Cf. A163511, A364257 (Dirichlet inverse), A364258, A364491, A364492, A364493.
Sequence in context: A340087 A239223 A143771 * A366283 A065331 A066262
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 16 2023
STATUS
approved