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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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 A180975 A210216

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

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Last modified April 3 23:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)