

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
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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



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:


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]]];


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



