A082086 Fixed points when A001414 is iterated and started at factorials of prime numbers.

2, 5, 5, 5, 13, 23, 61, 19, 5, 283, 5, 23, 13, 29, 7, 61, 947, 29, 137, 11, 353, 23, 199, 5, 47, 2381, 5, 103, 359, 13, 5, 5, 7, 5, 47, 19, 577, 7, 5, 29, 5, 5, 5, 41, 11, 23, 239, 7, 11, 5, 11, 5, 23, 11821, 31, 5, 5, 13669, 7, 193, 5, 991, 89, 7, 13, 18199, 131, 113, 20849

Offset: 1

Author

Labos Elemer, Apr 08 2003

Keywords

• nonn

Examples

			n=100, prime(100) = 541, start at 541!, the list is: {541!,...,46374,195,21,10,7} so a(100)=7.
		

Crossrefs

Cf. A008475, A082081, A000142, A000040, A000961.

Programs

Mathematica

sopfr[n_] := Total[Times @@@ FactorInteger[n]]; a[n_] := FixedPoint[sopfr, Prime[n]!]; Array[a, 100] (* Jean-François Alcover, May 06 2017 *)

Formula

a(n) = A029908(A000142(A000040(n))) = A029908(prime(n)!).