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

Author

Antti Karttunen, May 26 2021

Keywords

• nonn

Comments

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.

Links

• 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)

Crossrefs

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

Cf. also A344757.

Programs

PARI

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))); };

Formula

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