The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A016837 Primes reached after k iterations of sum of n and its prime divisors = t (where t replaces n in each iteration). 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Patrick asked what composite would produce 666 or 313 iterations. Carlos has also been working on the problem and asks if there is a run of 3 primes produced by consecutive composites. So original idea belongs to Patrick. This sequence was calculated by Enoch. LINKS Robert Israel, Table of n, a(n) for n = 2..10000 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 940 FORMULA Factor n, add n and its prime divisors. Sum = t, t replaces n, repeat until a prime is produced. EXAMPLE 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. 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 PROG (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 CROSSREFS Cf. A096461, A018845. Sequence in context: A128364 A281924 A054574 * A226218 A294087 A323137 Adjacent sequences:  A016834 A016835 A016836 * A016838 A016839 A016840 KEYWORD easy,nonn AUTHOR EXTENSIONS Corrected by Michel Marcus and Robert Israel, Jul 24 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 23 02:41 EDT 2021. Contains 347609 sequences. (Running on oeis4.)