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

1,4

Links

Table of n, a(n) for n=1..38.

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A238703 A185908 A234951 * A278493 A209334 A180975

Adjacent sequences: A291299 A291300 A291301 * A291303 A291304 A291305

Keyword

nonn,more

Author

N. J. A. Sloane, 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

Status

approved