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%I #9 Mar 22 2024 17:22:40
%S 1,4,8,18,16,32,54,100,64,72,162,128,294,144,256,500,216,486,288,400,
%T 512,432,1210,576,648,800,1024,1458,2028,2058,864,1176,2500,1800,1152,
%U 1296,1600,2048,4624,2000,1728,2352,1944,4374,6498,2304,2592,3200,4096,5292,4000
%N Euler totient function applied to the cubefull numbers (A036966).
%H Amiram Eldar, <a href="/A371412/b371412.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000010(A036966(n)).
%F Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/((p-1)^2*p)) = zeta(2)^2 * Product_{p prime} (1 - 2/p^2 + 1/p^3 + 3/p^4 + 1/p^5) = 1.65532418864085918623... .
%t Join[{1}, EulerPhi /@ Select[Range[20000], AllTrue[Last /@ FactorInteger[#], #1 > 2 &] &]]
%t (* or *)
%t f[n_] := Module[{f = FactorInteger[n], p, e}, If[n == 1, 1, p = f[[;;, 1]]; e = f[[;;, 2]]; If[Min[e] > 2, Times @@ ((p-1) * p^(e-1)), Nothing]]]; Array[f, 20000]
%o (PARI) lista(max) = {my(f); print1(1, ", "); for(k = 2, max, f = factor(k); if(vecmin(f[, 2]) > 2, print1(eulerphi(f), ", ")));}
%Y Cf. A000010, A013661, A036966, A098198.
%Y Similar sequences: A323333, A358039, A371413, A371414.
%K nonn,easy
%O 1,2
%A _Amiram Eldar_, Mar 22 2024
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