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 A321944 Starting from n, repeatedly compute the sum of the prime divisors until a fixed point or 0 is reached; a(n) is the number of terms, including n. 1
 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 3, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 2, 4, 2, 3, 1, 3, 1, 2, 4, 2, 3, 2, 1, 4, 3, 2, 1, 3, 1, 2, 3, 3, 1, 2, 2, 2, 3, 4, 1, 2, 3, 3, 3, 2, 1, 3, 1, 5, 3, 2, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is 1 + the number of iterations of n -> A008472(n) until n = A008472(n) or n=0. The fixed points are in A075860. For n>1 the fixed point is a prime number. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE For n=21: 21->{3,7} 3+7=10, 10->{2,5} 2+5=7, 7->{7} 7; 3 terms found {21,10,7}, therefore a(21) = 3. For n=2: 2->{2} 2, 1 term found {2}, therefore a(2) = 1. For n=1: 1->{} 0, 2 term found {1,0}, therefore a(1) = 2. MAPLE f:= proc(n) option remember;   if isprime(n) then 1   else 1+procname(convert(numtheory:-factorset(n), `+`))   fi end proc: f(1):= 2: map(f, [\$1..100]); # Robert Israel, Mar 30 2020 MATHEMATICA s[n_] := DivisorSum[n, # &, PrimeQ[#] &]; a[1] = 2; a[n_] := Length[ FixedPointList[s, n]] - 1; Array[a, 60, 0] (* Amiram Eldar, Dec 12 2018 *) PROG (C++) int Sum(int x){int acum=0, i=-1; for(; primes[++i]<=x; )if(!(x%primes[i])) acum+=primes[i]; return acum; } int a(int n){int cn=0, last=n; while(1){cn++; n=Sum(n); if(n==last)break; last=n; } return cn; } (PARI) a(n)={my(k=1); while(n&&!isprime(n), k++; n=vecsum(factor(n)[, 1])); k} \\ Andrew Howroyd, Dec 12 2018 CROSSREFS Cf. A008472, A075860, A002217. Sequence in context: A105103 A086669 A053574 * A065203 A230798 A266224 Adjacent sequences:  A321941 A321942 A321943 * A321945 A321946 A321947 KEYWORD nonn AUTHOR Wilmer Emiro Castrillon Calderon, Dec 12 2018 STATUS approved

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Last modified July 23 17:41 EDT 2021. Contains 346259 sequences. (Running on oeis4.)