A048126 Becomes prime or 4 after exactly 4 iterations of f(x) = sum of prime factors of x.

26, 33, 39, 44, 49, 51, 55, 65, 66, 70, 77, 78, 84, 91, 92, 95, 98, 100, 105, 110, 112, 114, 119, 120, 125, 126, 128, 129, 130, 132, 135, 140, 143, 144, 150, 154, 156, 160, 162, 168, 170, 180, 189, 192, 196, 200, 204, 205, 216, 217, 220, 225, 240, 242, 243

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

f(x) = sum of prime factors with multiplicity, so that f(1500) = 2+2+3+5+5+5 = 22.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Mathematica

spf[n_]:=Total[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]]; p4Q[n_] := Module[{lst=NestList[spf,n,4]},NoneTrue[Most[lst],PrimeQ] && NoneTrue[ Most[lst],#==4&]&&(PrimeQ[lst[[-1]]]||lst[[-1]]==4)]; Select[ Range[ 250],p4Q] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 17 2020 *)