A354358 Möbius transform of A124859.

1, 1, 1, 4, 1, 1, 1, 24, 4, 1, 1, 4, 1, 1, 1, 180, 1, 4, 1, 4, 1, 1, 1, 24, 4, 1, 24, 4, 1, 1, 1, 2100, 1, 1, 1, 16, 1, 1, 1, 24, 1, 1, 1, 4, 4, 1, 1, 180, 4, 4, 1, 4, 1, 24, 1, 24, 1, 1, 1, 4, 1, 1, 4, 27720, 1, 1, 1, 4, 1, 1, 1, 96, 1, 1, 4, 4, 1, 1, 1, 180, 180, 1, 1, 4, 1, 1, 1, 24, 1, 4, 1, 4, 1, 1, 1, 2100

Offset: 1

Author

Antti Karttunen, Jun 05 2022

Keywords

• nonn
• mult

Comments

Multiplicative because A124859 is.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A002110, A008683, A124859.

Cf. also A347379, A354359.

Programs

Mathematica

primorial[n_] := Product[Prime[i], {i, 1, n}]; primorial[0] = 1; f[p_, e_] := primorial[e] - primorial[e-1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 07 2023 *)

PARI

A124859(n) = { my(f=factor(n)); for(k=1, #f~, f[k, 1] = prod(j=1, f[k, 2], prime(j)); f[k, 2] = 1); factorback(f); }; \\ From A124859
A354358(n) = sumdiv(n,d,moebius(n/d)*A124859(d));

Formula

a(n) = Sum_{d|n} A008683(n/d) * A124859(d).

Multiplicative with a(p^e) = primorial(e) - primorial(e-1). - Sebastian Karlsson, Jul 30 2022