A039788 Numbers k such that phi(k) is equal to the product of (the sum of prime factors and the sum of exponents) of k.
9, 16, 35, 45, 150, 154, 234, 264
Offset: 1
Examples
45 is a term since phi(45) = 24, 45 = 3^2*5^1, (3+5)*(2+1) = 24.
Programs
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Mathematica
q[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;;, 1]]; e = f[[;;, 2]]; Times @@ ((p-1) * p^(e-1)) == Total[p] * Total[e]]; Select[Range[2, 300], q] (* Amiram Eldar, Jun 10 2025 *) -
PARI
for(n=1,10000000,f=factor(n);l=#f[,1];if(eulerphi(n)==sum(i=1,l,f[i,1])*sum(i=1,l,f[i,2]),print1(n,","))) (Ronaldo)
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PARI
isok(k) = if(k == 1, 0, my(f = factor(k)); eulerphi(f) == vecsum(f[,1]) * vecsum(f[,2])); \\ Amiram Eldar, Jun 10 2025
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