A354358 - OEIS

%I #17 Jan 07 2023 04:03:22

%S 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,

%T 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,

%U 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

%N Möbius transform of A124859.

%C Multiplicative because A124859 is.

%H Antti Karttunen, <a href="/A354358/b354358.txt">Table of n, a(n) for n = 1..20000</a>

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

%F Multiplicative with a(p^e) = primorial(e) - primorial(e-1). - _Sebastian Karlsson_, Jul 30 2022

%t 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 *)

%o (PARI)

%o 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

%o A354358(n) = sumdiv(n,d,moebius(n/d)*A124859(d));

%Y Cf. A002110, A008683, A124859.

%Y Cf. also A347379, A354359.

%K nonn,mult

%O 1,4

%A _Antti Karttunen_, Jun 05 2022