A039788 -id:A039788 - cp's OEIS frontend

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

Next term if it exists is greater than 100000.

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

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

Cf. A000010, A039697, A039788, A039789.

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 *)

isok(k) = if(k < 3, 0, my(f = factor(k-1)); eulerphi(k) == vecsum(f[,1]) * vecsum(f[,2])); \\ Amiram Eldar, Jun 10 2025

A039789 Integers k such that phi(k) is equal to the product of (the sum of prime factors and the sum of exponents) of k+1.

Original entry on oeis.org

7, 15, 62, 65, 76, 98, 260, 980

Offset: 1

Olivier Gérard

Next term if it exists is greater than 1500000. - Reiner Martin, May 20 2001
No further terms up to 20000000. - Harvey P. Dale, Apr 19 2013
a(9) > 10^10, if it exists. - Amiram Eldar, Jun 10 2025

			62 is a term since phi(62) = 30, 63 = 3^2*7^1, (3+7)*(2+1) = 30.

Cf. A000010, A039697, A039774, A039788.

epQ[n_]:=Module[{fi=Transpose[FactorInteger[n+1]]},EulerPhi[n]== Total[ First[fi]]* Total[Last[fi]]]; Select[Range[1000],epQ] (* Harvey P. Dale, Apr 19 2013 *)

isok(k) = my(f=factor(k+1)); eulerphi(k) == vecsum(f[,1]) * vecsum(f[,2]); \\ Michel Marcus, Oct 30 2022

cp's OEIS Frontend

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.

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