A082089 a(n)-th prime is the fixed point if function A008472[=sum of prime factors with no repetition] is iterated when started at factorial of n-th prime.

1, 3, 4, 7, 2, 13, 11, 3, 4, 3, 4, 45, 1, 60, 14, 4, 3, 3, 21, 1, 4, 4, 6, 3, 4, 3, 2, 4, 6, 2, 4, 4, 4, 4, 105, 4, 4, 3, 4, 4, 3, 4, 3, 4, 1, 4, 8, 2, 2, 19, 3, 1, 20, 14, 4, 20, 52, 4, 4, 977, 1, 3, 65, 1108, 1, 2, 46, 3, 3, 1, 3, 1, 2, 4, 829, 2, 25, 3, 8, 25, 4, 378, 3, 3, 29, 3, 6, 8, 1, 1, 28

Offset: 2

Author

Labos Elemer, Apr 09 2003

Keywords

• nonn

Comments

a(n) < n holds usually, except few large values arising unexpectedly.

Examples

			n=100, p(100)=541, starts at factorial of 100th prime and ends in 24133, the 2687th prime, so a(100)=2687;
n=99, initial value=523!, fixed point is 19, the 8th prime, a(99)=8.
		

Crossrefs

Cf. A008472, A034387, A007504, A075860, A082087, A082088.

Programs

Mathematica

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] sopf[x_] := Apply[Plus, ba[x]] Table[PrimePi[FixedPoint[sopf, Prime[w]! ]], {w, 2, 100}]

Formula

a(n) = A000720(A082087(A000142(A000040(n)))) = pi(A082087(p(n)!)).