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.

3, 5, 9, 25, 31, 57, 116, 144, 154, 288, 372, 414, 624, 792, 10032

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• more

Comments

Next term if it exists is greater than 100000.

a(16) > 10^10, if it exists. - Amiram Eldar, Jun 10 2025

Examples

			25 is a term since phi(25) = 20, 24 = 2^3*3^1, (2+3)*(3+1) = 20.
		

Crossrefs

Cf. A000010, A039697, A039788, A039789.

Programs

Mathematica

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 *)

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