A344024 a(n) = A003415(A001615(n)).

0, 1, 4, 5, 5, 16, 12, 16, 16, 21, 16, 44, 9, 44, 44, 44, 21, 60, 24, 60, 80, 60, 44, 112, 31, 41, 60, 112, 31, 156, 80, 112, 112, 81, 112, 156, 21, 92, 92, 156, 41, 272, 48, 156, 156, 156, 112, 272, 92, 123, 156, 124, 81, 216, 156, 272, 176, 123, 92, 384, 33, 272, 272, 272, 124, 384, 72, 216, 272, 384, 156, 384, 39, 101

Offset: 1

Author

Antti Karttunen, May 09 2021

Keywords

• nonn

Comments

The first nonsquarefree numbers for which this sequence coincides with A342925 are 868, 920, 952, 4260, 4452, 4692, 5060, 5172, ...

Links

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

Crossrefs

Cf. A001615, A003415, A005117.

Cf. also A342925.

Programs

Mathematica

{0}~Join~Array[If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &[# Product[1 + 1/p, {p, FactorInteger[#][[All, 1]]}] ] &, 73, 2] (* Michael De Vlieger, May 16 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
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A344024(n) = A003415(A001615(n));

Formula

a(A005117(n)) = A342925(A005117(n)) for all n.