A370784 a(n) is the denominator of the sum of the reciprocals of the squarefree divisors of the powerful part of n.
1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 5, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 7, 5, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 5, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- Rafael Jakimczuk, Arithmetical Functions over the Powerful Part of an Integer, ResearchGate, 2024.
Programs
-
Mathematica
a[n_] := Denominator[Times @@ (1 + 1/Select[FactorInteger[n], Last[#] > 1 &][[;; , 1]])]; Array[a, 100]
-
PARI
a(n) = {my(f = factor(n)); denominator(prod(i = 1, #f~, if(f[i,2] == 1, 1, 1 + 1/f[i,1])));}