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A075860 a(n) is the fixed point reached by the sum of divisors of n without multiplicity (with the convention a(1)=0). 9
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 (list; graph; refs; listen; history; text; internal format)
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] (* Jean-Fran├žois 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,changed

AUTHOR

Joseph L. Pe, Oct 15 2002

EXTENSIONS

Better description from Labos Elemer, Apr 09 2003

STATUS

approved

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Last modified April 3 17:03 EDT 2020. Contains 333197 sequences. (Running on oeis4.)