This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A039774 #10 Jun 10 2025 03:27:08
%S A039774 3,5,9,25,31,57,116,144,154,288,372,414,624,792,10032
%N A039774 Numbers k such that phi(k) is equal to the product of (the sum of prime factors and the sum of exponents) of k-1.
%C A039774 Next term if it exists is greater than 100000.
%C A039774 a(16) > 10^10, if it exists. - _Amiram Eldar_, Jun 10 2025
%e A039774 25 is a term since phi(25) = 20, 24 = 2^3*3^1, (2+3)*(3+1) = 20.
%t A039774 s[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;;, 1]]; e = f[[;;, 2]]; Total[p] * Total[e]]; Select[Range[3, 12000], EulerPhi[#] == s[#-1] &] (* _Amiram Eldar_, Jun 10 2025 *)
%o A039774 (PARI) isok(k) = if(k < 3, 0, my(f = factor(k-1)); eulerphi(k) == vecsum(f[,1]) * vecsum(f[,2])); \\ _Amiram Eldar_, Jun 10 2025
%Y A039774 Cf. A000010, A039697, A039788, A039789.
%K A039774 nonn,more
%O A039774 1,1
%A A039774 _Olivier Gérard_