A342915 a(n) = gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).

1, 3, 4, 1, 6, 1, 8, 3, 2, 1, 12, 1, 14, 3, 8, 1, 18, 1, 20, 3, 2, 1, 24, 1, 2, 3, 4, 1, 30, 1, 32, 3, 2, 1, 12, 1, 38, 3, 8, 1, 42, 1, 44, 9, 2, 1, 48, 1, 2, 3, 4, 1, 54, 1, 8, 3, 2, 1, 60, 1, 62, 3, 32, 1, 6, 1, 68, 3, 2, 1, 72, 1, 74, 3, 4, 1, 6, 1, 80, 9, 2, 1, 84, 1, 2, 3, 8, 1, 90, 1, 4, 3, 2, 1, 24, 1, 98, 3, 4, 1, 102

Offset: 1

Author

Antti Karttunen, Mar 29 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A001615, A342916, A342917.

Cf. also A049559, A342458.

After n=1 differs from A143771 for the first time at n=44, where a(44) = 9, while A143771(44) = 3.

Programs

Mathematica

psi[n_] := If[n==1, 1, Times @@ ((#1+1)*#1^(#2-1)& @@@ FactorInteger[n])];
a[n_] := GCD[n+1, psi[n]];
Array[a, 105] (* Jean-François Alcover, Dec 22 2021 *)

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
A342915(n) = gcd(1+n,A001615(n));

Formula

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

a(n) = (1+n) / A342916(n) = A001615(n) / A342917(n).