A342917 a(n) = A001615(n) / gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).

1, 1, 1, 6, 1, 12, 1, 4, 6, 18, 1, 24, 1, 8, 3, 24, 1, 36, 1, 12, 16, 36, 1, 48, 15, 14, 9, 48, 1, 72, 1, 16, 24, 54, 4, 72, 1, 20, 7, 72, 1, 96, 1, 8, 36, 72, 1, 96, 28, 30, 18, 84, 1, 108, 9, 32, 40, 90, 1, 144, 1, 32, 3, 96, 14, 144, 1, 36, 48, 144, 1, 144, 1, 38, 30, 120, 16, 168, 1, 16, 54, 126, 1, 192, 54, 44, 15, 144

Offset: 1

Author

Antti Karttunen, Mar 29 2021

Keywords

• nonn
• look

Comments

The scatter plot shows two distinct "fans" separated by a gap. Why?

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A001615, A342915, A342916.

Cf. also A160595.

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
A342917(n) = { my(u=A001615(n)); (u/gcd(1+n,u)); };

Formula

a(n) = A001615(n) / A342915(n) = A001615(n) / gcd(1+n, A001615(n)).