A364257 -id:A364257 - cp's OEIS frontend

A364255 a(n) = gcd(n, A163511(n)).

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

Antti Karttunen, Jul 16 2023

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16383
Index entries for sequences related to binary expansion of n

Cf. A163511, A364257 (Dirichlet inverse), A364258, A364491, A364492, A364493.

Cf. also A364254, A364256, A339969, A364500, A364949.

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

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

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)

A364957 Dirichlet inverse of A365463.

Original entry on oeis.org

1, -2, -3, 3, -1, 6, -1, -12, 0, 3, -1, -9, -1, 2, 3, 35, -1, 0, -1, -10, 3, 3, -1, 36, -24, 2, 0, -3, -1, -9, -1, -82, 3, 2, -5, 0, -1, 2, 3, 37, -1, -6, -1, -10, 0, 3, -1, -105, 0, 46, 3, -6, -1, 0, -9, 18, 3, 3, -1, 30, -1, 2, 0, 226, -3, -9, -1, -6, 3, 12, -1, 0, -1, 2, 72, -3, 1, -6, -1, -127, 0, 3, -1, 9, -3, 2, 3

Offset: 1

Antti Karttunen, Sep 16 2023

sign

Antti Karttunen, Table of n, a(n) for n = 1..19683

Cf. A356867, A365463.

Cf. also A364257.

\\ Uses also code from A356867:
A365463(n) = gcd(n, A356867(n));
memoA364957 = Map();
A364957(n) = if(1==n,1,my(v); if(mapisdefined(memoA364957,n,&v), v, v = -sumdiv(n,d,if(dA365463(n/d)*A364957(d),0)); mapput(memoA364957,n,v); (v)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA365463(n/d) * a(d).

A366258 Dirichlet inverse of A366283, where A366283(n) = gcd(n, A366275(n)).

Original entry on oeis.org

1, -2, -3, 0, -1, 6, -1, 0, 0, 2, -1, 0, -1, 2, 5, 0, -1, 0, -1, 0, 3, 2, -1, 0, -24, 2, 26, 0, -1, -10, -1, 0, 3, 2, -3, 0, -1, 2, 3, 0, -1, -6, -1, 0, -6, 2, -1, 0, 0, 48, 5, 0, -1, -52, -53, 0, 5, 2, -1, 0, -1, 2, 8, 0, 1, -6, -1, 0, 3, 6, -1, 0, -1, 2, 128, 0, -5, -6, -1, 0, -78, 2, -1, 0, -3, 2, 3, 0, -1, 12

Offset: 1

Antti Karttunen, Oct 07 2023

sign

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to binary expansion of n

Cf. A366275, A366283, A366259 (rgs-transform).

Cf. also A364257.

\\ Needs also the program given in A366275:
A366283(n) = gcd(n,A366275(n));
memoA366258 = Map();
A366258(n) = if(1==n,1,my(v); if(mapisdefined(memoA366258,n,&v), v, v = -sumdiv(n,d,if(dA366283(n/d)*A366258(d),0)); mapput(memoA366258,n,v); (v)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA366283(n/d) * a(d).

cp's OEIS Frontend

A364255 a(n) = gcd(n, A163511(n)).

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A364957 Dirichlet inverse of A365463.

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A366258 Dirichlet inverse of A366283, where A366283(n) = gcd(n, A366275(n)).

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