

A075860


a(n) is the fixed point reached by the sum of divisors of n without multiplicity (with the convention a(1)=0).


10



0, 2, 3, 2, 5, 5, 7, 2, 3, 7, 11, 5, 13, 3, 2, 2, 17, 5, 19, 7, 7, 13, 23, 5, 5, 2, 3, 3, 29, 7, 31, 2, 3, 19, 5, 5, 37, 7, 2, 7, 41, 5, 43, 13, 2, 5, 47, 5, 7, 7, 7, 2, 53, 5, 2, 3, 13, 31, 59, 7, 61, 3, 7, 2, 5, 2, 67, 19, 2, 3, 71, 5, 73, 2, 2, 7, 5, 5, 79, 7, 3, 43, 83, 5, 13, 2, 2, 13, 89
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OFFSET

1,2


COMMENTS

For n>1, the sequence reaches a fixed point, which is prime.
From Robert Israel, Mar 31 2020: (Start)
a(n) = n if n is prime.
a(n) = n/2 + 2 if n is in A108605.
a(n) = n/4 + 2 if n is in 4*A001359. (End)


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


EXAMPLE

Starting with 60 = 2^2 * 3 * 5 as the first term, add the prime factors of 60 to get the second term = 2 + 3 + 5 = 10. Then add the prime factors of 10 = 2 * 5 to get the third term = 2 + 5 = 7, which is prime. (Successive terms of the sequence will be equal to 7.) Hence a(60) = 7.


MAPLE

f:= proc(n) option remember;
if isprime(n) then n
else procname(convert(numtheory:factorset(n), `+`))
fi
end proc:
f(1):= 0:
map(f, [$1..100]); # Robert Israel, Mar 31 2020


MATHEMATICA

f[n_] := Module[{a}, a = n; While[ !PrimeQ[a], a = Apply[Plus, Transpose[FactorInteger[a]][[1]]]]; a]; Table[f[i], {i, 2, 100}]
(* Second program: *)
a[n_] := If[n == 1, 0, FixedPoint[Total[FactorInteger[#][[All, 1]]]&, n]];
Array[a, 100] (* JeanFrançois Alcover, Apr 01 2020 *)


CROSSREFS

A008472(n) is sum of prime divisors of n. Cf. A029908.
Sequence in context: A141346 A095402 A086294 * A323171 A008472 A318675
Adjacent sequences: A075857 A075858 A075859 * A075861 A075862 A075863


KEYWORD

nonn,look


AUTHOR

Joseph L. Pe, Oct 15 2002


EXTENSIONS

Better description from Labos Elemer, Apr 09 2003


STATUS

approved



