A358216 Inverse Möbius transform of A327936, where A327936 is multiplicative with a(p^e) = p if e >= p, otherwise 1.
1, 2, 2, 4, 2, 4, 2, 6, 3, 4, 2, 8, 2, 4, 4, 8, 2, 6, 2, 8, 4, 4, 2, 12, 3, 4, 6, 8, 2, 8, 2, 10, 4, 4, 4, 12, 2, 4, 4, 12, 2, 8, 2, 8, 6, 4, 2, 16, 3, 6, 4, 8, 2, 12, 4, 12, 4, 4, 2, 16, 2, 4, 6, 12, 4, 8, 2, 8, 4, 8, 2, 18, 2, 4, 6, 8, 4, 8, 2, 16, 9, 4, 2, 16, 4, 4, 4, 12, 2, 12, 4, 8, 4, 4, 4, 20, 2, 6, 6, 12
Offset: 1
Links
- Antti Karttunen, Table of n, a(n) for n = 1..22680
- Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000
Programs
-
Mathematica
f[p_, e_] := If[e < p, e + 1, p*(e - p + 2)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 30 2022 *)
-
PARI
A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k,2] = (f[k,2]>=f[k,1])); factorback(f); }; A358216(n) = sumdiv(n,d,A327936(d));
Formula
a(n) = Sum_{d|n} A327936(d).
For all n >= 1, a(n) >= A000005(n).
Multiplicative with a(p^e) = e + 1 if e < p, and p*(e - p + 2) otherwise. - Amiram Eldar, Nov 30 2022
Comments