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

1,4

Comments

Multiplicative because A124859 is.

Links

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

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

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 *)

Prog

(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));

Crossrefs

Cf. A002110, A008683, A124859.

Cf. also A347379, A354359.

Sequence in context: A265679 A348989 A362297 * A112622 A183104 A183102

Adjacent sequences: A354355 A354356 A354357 * A354359 A354360 A354361

Keyword

nonn,mult

Author

Antti Karttunen, Jun 05 2022

Status

approved