A130790 - OEIS

%I #9 Nov 04 2019 02:32:38

%S 0,1,1,2,2,2,1,2,3,3,3,2,2,4,4,3,4,3,4,4,2,4,3,3,2,2,3,4,2,3,4,4,2,5,

%T 3,3,4,2,4,5,4,3,4,2,3,4,5,4,4,4,4,4,3,2,1,5,5,3,5,4,6,3,3,5,4,5,5,4,

%U 6,5,3,5,5,5,4,5,3,4,2,3,5,5,6,2,4,4,3,4,5,6,5,5,2,4,5,3,5,4,5,3

%N Number of nodes in the Lucas-Pratt primality tree rooted at prime(n).

%C The primality tree starts at an odd prime at the root node. The branches of each node are the odd primes that divide the value of (the node minus 1). The length of the longest branch is related to A126805. Following the branch with the largest label gives A083647.

%H J. Bayless, <a href="http://dx.doi.org/10.1090/S0025-5718-07-02002-9">The Lucas-Pratt primality tree</a>, Math. Comp. vol 77 (2008) 495-502.

%o (PARI) LP(p) = my(f=factor(p-1)); if(p <= 2, 0, 1+vecsum(vector(#f~, k, LP(f[k,1]))));

%o a(n) = LP(prime(n)); \\ _Daniel Suteu_, Nov 03 2019

%Y Cf. A083647, A126805.

%Y Cf. A037231 (primes which set a new record).

%K easy,nonn

%O 1,4

%A _R. J. Mathar_, Jul 15 2007, Mar 07 2008