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 A029912 Start with n; repeatedly sum prime factors (counted with multiplicity) and add 1, until reach 1, 6 or a prime. 1
 1, 3, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 11, 7, 7, 7, 11, 7, 7, 7, 11, 11, 11, 11, 7, 7, 13, 11, 7, 7, 17, 7, 13, 13, 7, 7, 7, 7, 7, 7, 7, 13, 11, 7, 7, 7, 17, 7, 23, 11, 13, 13, 7, 7, 7, 13, 19, 17, 7, 7, 7, 7, 13, 13, 7, 7, 7, 7, 19, 19, 7, 7, 13, 7, 7, 7, 23, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If p is in A023200 then a(3*p) = p+4. It appears that all n > 35 such that a(n) > n/3 are 3*p for p in A023200. - Robert Israel, Dec 18 2019 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 20 -> 2+2+5+1 = 10 -> 2+5+1 = 8 -> 2+2+2+1 = 7 so a(20)=7. MAPLE f:= proc(n) option remember; local v; v:= add(t[1]*t[2], t=ifactors(n)[2])+1; if v = 1 or v = 6 or isprime(v) then return v fi; procname(v) end proc: map(f, [\$1..100]); # Robert Israel, Dec 18 2019 MATHEMATICA a[n_] := a[n] = If[n==1, 1, Module[{v}, v = Sum[t[[1]]*t[[2]], {t, FactorInteger[n]}]+1; If[v==1 || v==6 || PrimeQ[v], Return[v]]; a[v]]]; a /@ Range[100] (* Jean-François Alcover, Aug 21 2022, after Robert Israel *) CROSSREFS Sequence in context: A143082 A330917 A330912 * A272756 A322350 A205560 Adjacent sequences: A029909 A029910 A029911 * A029913 A029914 A029915 KEYWORD nonn AUTHOR Dann Toliver STATUS approved

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Last modified December 5 05:37 EST 2023. Contains 367575 sequences. (Running on oeis4.)