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.

A358216 Inverse Möbius transform of A327936, where A327936 is multiplicative with a(p^e) = p if e >= p, otherwise 1.

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%I A358216 #12 Dec 01 2022 08:56:50
%S A358216 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,
%T A358216 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,
%U A358216 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
%N A358216 Inverse Möbius transform of A327936, where A327936 is multiplicative with a(p^e) = p if e >= p, otherwise 1.
%C A358216 Multiplicative because A327936 is.
%H A358216 Antti Karttunen, <a href="/A358216/b358216.txt">Table of n, a(n) for n = 1..22680</a>
%H A358216 Antti Karttunen, <a href="/A358216/a358216.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A358216 a(n) = Sum_{d|n} A327936(d).
%F A358216 For all n >= 0, a(A276086(n)) = A324655(n).
%F A358216 For all n >= 1, a(n) >= A000005(n).
%F A358216 Multiplicative with a(p^e) = e + 1 if e < p, and p*(e - p + 2) otherwise. - _Amiram Eldar_, Nov 30 2022
%t A358216 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 *)
%o A358216 (PARI)
%o A358216 A327936(n) = { my(f = factor(n)); for(k=1, #f~, f[k,2] = (f[k,2]>=f[k,1])); factorback(f); };
%o A358216 A358216(n) = sumdiv(n,d,A327936(d));
%Y A358216 Cf. A000005, A276086, A324655, A327936.
%K A358216 nonn,mult
%O A358216 1,2
%A A358216 _Antti Karttunen_, Nov 30 2022