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%I #17 Nov 10 2022 07:42:30
%S 1,2,2,4,4,4,6,8,4,8,10,8,12,12,8,16,16,8,18,16,12,20,22,16,16,24,8,
%T 24,28,16,30,32,20,32,24,16,36,36,24,32,40,24,42,40,16,44,46,32,36,32,
%U 32,48,52,16,40,48,36,56,58,32,60,60,24,64,48,40,66,64,44,48,70,32,72,72,32,72,60,48,78,64,16,80,82,48,64
%N Fully multiplicative with a(2) = 2 and a(p) = p-1 for odd primes p.
%H Antti Karttunen, <a href="/A333787/b333787.txt">Table of n, a(n) for n = 1..16384</a>
%F Multiplicative with a(p^e) = (p-A000035(p))^e.
%F a(n) = A003958(n) * A006519(n).
%F Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^4/(210*zeta(3)) = (3/4) * A068468 = 0.385882... . - _Amiram Eldar_, Nov 10 2022
%t Array[If[# == 1, 1, Apply[Times, FactorInteger[#] /. {p_Integer, e_Integer} :> If[p == 2, 2, p - 1]^e]] &, 85] (* _Michael De Vlieger_, Apr 15 2020 *)
%o (PARI) A333787(n) = { my(f=factor(n)); for(i=1,#f~,f[i,1] -= (f[i,1]%2)); factorback(f); };
%Y Cf. A000035, A003958, A006519, A068468.
%Y Cf. also A329697.
%K nonn,mult
%O 1,2
%A _Antti Karttunen_, Apr 07 2020
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