A344757 -id:A344757 - cp's OEIS frontend

A344697 a(n) = A001615(n) / gcd(sigma(n), A001615(n)).

1, 1, 1, 6, 1, 1, 1, 4, 12, 1, 1, 6, 1, 1, 1, 24, 1, 12, 1, 6, 1, 1, 1, 4, 30, 1, 9, 6, 1, 1, 1, 16, 1, 1, 1, 72, 1, 1, 1, 4, 1, 1, 1, 6, 12, 1, 1, 24, 56, 30, 1, 6, 1, 9, 1, 4, 1, 1, 1, 6, 1, 1, 12, 96, 1, 1, 1, 6, 1, 1, 1, 48, 1, 1, 30, 6, 1, 1, 1, 24, 108, 1, 1, 6, 1, 1, 1, 4, 1, 12, 1, 6, 1, 1, 1, 16, 1, 56, 12, 180

Offset: 1

Antti Karttunen, May 26 2021

nonn

This is not multiplicative. The first point where a(m*n) = a(m)*a(n) does not hold for coprime m and n is 108 = 4*27, where a(108) = 27, although a(4) = 6 and a(27) = 9. See A344702.

Antti Karttunen, Table of n, a(n) for n = 1..10404
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences related to sigma(n)

Cf. A000203, A001615, A005117, A344695, A344696, A344699, A344702.

Cf. also A344757.

A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A344697(n) = { my(u=A001615(n)); (u/gcd(u,sigma(n))); };

a(n) = A001615(n) / A344695(n).

A344756 a(n) = A003415(n) / gcd(A003415(n), A069359(n)).

Original entry on oeis.org

1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 8, 1, 1, 1, 4, 1, 7, 1, 12, 1, 1, 1, 11, 2, 1, 3, 16, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 17, 1, 1, 1, 24, 13, 1, 1, 14, 2, 9, 1, 28, 1, 9, 1, 23, 1, 1, 1, 46, 1, 1, 17, 6, 1, 1, 1, 36, 1, 1, 1, 13, 1, 1, 11, 40, 1, 1, 1, 22, 4, 1, 1, 62, 1, 1, 1, 35, 1, 41, 1, 48, 1, 1, 1, 17, 1, 11, 25

Offset: 2

Antti Karttunen, May 28 2021

nonn

Antti Karttunen, Table of n, a(n) for n = 2..12012
Antti Karttunen, Data supplement: n, a(n) computed for n = 2..65537

Cf. A003415, A005117 (for n > 1 gives the positions of ones), A069359, A340070, A344757.

Cf. also A344696.

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A069359(n) = (n*sumdiv(n, d, isprime(d)/d)); \\ From A069359
A344756(n) = { my(u=A003415(n)); (u/gcd(u,A069359(n))); };

a(n) = A003415(n) / A340070(n) = A003415(n) / gcd(A003415(n), A069359(n)).

cp's OEIS Frontend

A344697 a(n) = A001615(n) / gcd(sigma(n), A001615(n)).

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