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