cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A354358 Möbius transform of A124859.

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%I A354358 #17 Jan 07 2023 04:03:22
%S A354358 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 A354358 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 A354358 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 A354358 Möbius transform of A124859.
%C A354358 Multiplicative because A124859 is.
%H A354358 Antti Karttunen, <a href="/A354358/b354358.txt">Table of n, a(n) for n = 1..20000</a>
%F A354358 a(n) = Sum_{d|n} A008683(n/d) * A124859(d).
%F A354358 Multiplicative with a(p^e) = primorial(e) - primorial(e-1). - _Sebastian Karlsson_, Jul 30 2022
%t A354358 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 A354358 (PARI)
%o A354358 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 A354358(n) = sumdiv(n,d,moebius(n/d)*A124859(d));
%Y A354358 Cf. A002110, A008683, A124859.
%Y A354358 Cf. also A347379, A354359.
%K A354358 nonn,mult
%O A354358 1,4
%A A354358 _Antti Karttunen_, Jun 05 2022