A291302 a(n) = number of steps to reach a prime when x -> sigma(x)-1 is repeatedly applied to the product of the first n primes, or -1 if no prime is ever reached.

0, 1, 1, 2, 1, 3, 3, 1, 3, 4, 46, 57, 7, 9, 17, 1, 45, 1, 33, 8, 10, 4, 3, 32, 6, 47, 17, 21, 41, 17, 12, 11, 10, 31, 74, 25, 99, 11

Offset: 1

Author

N. J. A. Sloane, Aug 31 2017

Keywords

• nonn
• more

Examples

			2*3*5*7*11*13 = 30030 -> 96767 -> 111359 -> 117239 takes three steps to reach a prime, so a(6) = 3.
		

Crossrefs

Cf. A039654, A039653, A291301 (the prime reached).

Programs

Maple

A291302 := proc(n)
    local a,x ;
    a := 0 ;
    x := mul(ithprime(i),i=1..n) ;
    while not isprime(x) do
        x := numtheory[sigma](x)-1 ;
        a := a+1 ;
    end do:
    a ;
end proc: # R. J. Mathar, Sep 12 2017

Mathematica

p[n_]:=Times@@Prime/@Range[n];f[n_]:=DivisorSigma[1,n]-1;
a[n_]:=Length[NestWhileList[f,p[n],CompositeQ]]-1;a/@Range[34] (* Ivan N. Ianakiev, Sep 01 2017 *)

Python

from sympy import primorial, isprime, divisor_sigma
def A291302(n):
    m, c = primorial(n), 0
    while not isprime(m):
        m = divisor_sigma(m) - 1
        c += 1
    return c # Chai Wah Wu, Aug 31 2017

Extensions

a(11)-a(35) from Chai Wah Wu, Aug 31 2017

a(36)-a(38) from Ivan N. Ianakiev, Sep 01 2017