A342916 a(n) = (1+n) / gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).

2, 1, 1, 5, 1, 7, 1, 3, 5, 11, 1, 13, 1, 5, 2, 17, 1, 19, 1, 7, 11, 23, 1, 25, 13, 9, 7, 29, 1, 31, 1, 11, 17, 35, 3, 37, 1, 13, 5, 41, 1, 43, 1, 5, 23, 47, 1, 49, 25, 17, 13, 53, 1, 55, 7, 19, 29, 59, 1, 61, 1, 21, 2, 65, 11, 67, 1, 23, 35, 71, 1, 73, 1, 25, 19, 77, 13, 79, 1, 9, 41, 83, 1, 85, 43, 29, 11, 89, 1, 91, 23, 31

Offset: 1

Author

Antti Karttunen, Mar 29 2021

Keywords

• nonn

Comments

It is conjectured that a(n) = 1 only when n is a prime, A000040. See Thomas Ordowski's May 21 2017 problem in A001615.

Links

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

Crossrefs

Cf. A000040, A001615, A342915, A342917.

Cf. also A160596.

After n=1 differs from A342918 for the first time at n=44, where a(44) = 5, while A342918(44) = 15.

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
A342916(n) = ((1+n)/gcd(1+n,A001615(n)));

Formula

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

Extensions

Incorrect A-number in the formula corrected by Antti Karttunen, May 31 2021