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.

A342007 Multiplicative with a(p^e) = p^floor(e/p).

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%I A342007 #15 Nov 07 2022 07:40:27
%S A342007 1,1,1,2,1,1,1,2,1,1,1,2,1,1,1,4,1,1,1,2,1,1,1,2,1,1,3,2,1,1,1,4,1,1,
%T A342007 1,2,1,1,1,2,1,1,1,2,1,1,1,4,1,1,1,2,1,3,1,2,1,1,1,2,1,1,1,8,1,1,1,2,
%U A342007 1,1,1,2,1,1,1,2,1,1,1,4,3,1,1,2,1,1,1,2,1,1,1,2,1,1,1,4,1,1,1,2,1,1,1,2,1
%N A342007 Multiplicative with a(p^e) = p^floor(e/p).
%H A342007 Antti Karttunen, <a href="/A342007/b342007.txt">Table of n, a(n) for n = 1..65537</a>
%F A342007 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 + (p-1)/(p^p-p)) = 1.6270951877598772517... . - _Amiram Eldar_, Nov 07 2022
%t A342007 Array[Times @@ Map[#1^Floor[#2/#1] & @@ # &, FactorInteger[#]] &, 105] (* _Michael De Vlieger_, Mar 12 2021 *)
%o A342007 (PARI) A342007(n) = { my(f = factor(n)); for(k=1, #f~, f[k, 2] = floor(f[k, 2]/f[k, 1])); factorback(f); };
%Y A342007 Cf. A327936, A327938, A327939, A341997, A342017 [= a(A276086(n))].
%K A342007 nonn,mult
%O A342007 1,4
%A A342007 _Antti Karttunen_, Mar 04 2021