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%I #9 Mar 22 2024 17:22:56
%S 1,12,24,36,48,96,108,150,192,432,324,384,392,864,768,750,1296,972,
%T 1728,1800,1536,2592,1452,3456,3888,3600,3072,2916,2366,2744,5184,
%U 4704,3750,5400,6912,7776,7200,6144,5202,9000,10368,9408,11664,8748,7220,13824,15552
%N Dedekind psi function applied to the cubefull numbers (A036966).
%H Amiram Eldar, <a href="/A371413/b371413.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A001615(A036966(n)).
%F Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/((p^2-1)*p)) = 1.231291... (A065487).
%t psi[n_] := n * Times @@ (1 + 1/FactorInteger[n][[;; , 1]]); psi[1] = 1; Join[{1}, psi /@ 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) dedpsi(f) = prod(i = 1, #f~, (f[i, 1] + 1) * f[i, 1]^(f[i, 2]-1));
%o lista(max) = {my(f); print1(1, ", "); for(k = 2, max, f = factor(k); if(vecmin(f[, 2]) > 2, print1(dedpsi(f), ", "))); }
%Y Cf. A001615, A036966, A065464.
%Y Similar sequences: A323332, A371412, A371415.
%K nonn,easy
%O 1,2
%A _Amiram Eldar_, Mar 22 2024
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