A016837 Primes reached after k iterations of sum of n and its prime divisors = t (where t replaces n in each iteration).
23, 11, 23, 17, 11, 23, 23, 23, 17, 47, 19, 41, 23, 23, 47, 53, 41, 59, 29, 31, 47, 71, 47, 47, 41, 71, 71, 89, 71, 167, 83, 47, 53, 47, 71, 113, 59, 71, 71, 269, 83, 131, 59, 167, 71, 167, 59, 149, 167, 71, 167, 191, 83, 71, 167, 79, 89, 179, 251, 227, 167, 149, 149, 83, 269, 239, 89, 167, 251, 263, 251, 251, 113, 239, 149, 167
Offset: 2
Examples
Starting from 4, 4=2*2, so 4+2+2=8. 8=2*2*2 so 8+2+2+2=14. 14=2*7 so 14+2+7=23, prime is 23 in 3 iterations.
Links
- Robert Israel, Table of n, a(n) for n = 2..10000
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 940
Programs
-
Maple
f:= proc(n) option remember; local t; t:= n + add(f[1]*f[2],f=ifactors(n)[2]); if isprime(t) then return t else f(t) fi; end proc: map(f, [$2 .. 100]); # Robert Israel, Jul 24 2015
-
Mathematica
a[n_] := a[n] = Module[{t, f = FactorInteger[n]}, t = n + f[[All, 1]].f[[All, 2]]; If[PrimeQ[t], Return[t], a[t]]]; Table[a[n], {n, 2, 100}] (* Jean-François Alcover, Sep 16 2022 *) -
PARI
sfpn(n) = {my(f = factor(n)); n + sum(k=1, #f~, f[k,1]*f[k,2]);} a(n) = {while (! isprime(t=sfpn(n)), n=t); t;} \\ Michel Marcus, Jul 24 2015
Formula
Factor n, add n and its prime divisors. Sum = t, t replaces n, repeat until a prime is produced.
Extensions
Corrected by Michel Marcus and Robert Israel, Jul 24 2015
Comments