A291302 - OEIS

%I #23 Sep 12 2017 12:30:20

%S 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,

%T 17,12,11,10,31,74,25,99,11

%N 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.

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

%p A291302 := proc(n)

%p     local a,x ;

%p     a := 0 ;

%p     x := mul(ithprime(i),i=1..n) ;

%p     while not isprime(x) do

%p         x := numtheory[sigma](x)-1 ;

%p         a := a+1 ;

%p     end do:

%p     a ;

%p end proc: # _R. J. Mathar_, Sep 12 2017

%t p[n_]:=Times@@Prime/@Range[n];f[n_]:=DivisorSigma[1,n]-1;

%t a[n_]:=Length[NestWhileList[f,p[n],CompositeQ]]-1;a/@Range[34] (* _Ivan N. Ianakiev_, Sep 01 2017 *)

%o (Python)

%o from sympy import primorial, isprime, divisor_sigma

%o def A291302(n):

%o     m, c = primorial(n), 0

%o     while not isprime(m):

%o         m = divisor_sigma(m) - 1

%o         c += 1

%o     return c # _Chai Wah Wu_, Aug 31 2017

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

%K nonn,more

%O 1,4

%A _N. J. A. Sloane_, Aug 31 2017

%E a(11)-a(35) from _Chai Wah Wu_, Aug 31 2017

%E a(36)-a(38) from _Ivan N. Ianakiev_, Sep 01 2017