

A002217


Starting with n, repeatedly calculate the sum of prime factors (with repetition) of the previous term, until reaching 0 or a fixed point: a(n) is the number of terms in the resulting sequence.
(Formerly M0150 N0060)


6



2, 1, 1, 1, 1, 2, 1, 3, 3, 2, 1, 2, 1, 4, 4, 4, 1, 4, 1, 4, 3, 2, 1, 4, 3, 5, 4, 2, 1, 3, 1, 3, 5, 2, 3, 3, 1, 4, 5, 2, 1, 3, 1, 5, 2, 4, 1, 2, 5, 3, 5, 2, 1, 2, 5, 2, 3, 2, 1, 3, 1, 6, 2, 3, 5, 5, 1, 4, 6, 5, 1, 3, 1, 6, 2, 2, 5, 5, 1, 2, 3, 2, 1, 5, 3, 3, 4, 2, 1, 2, 5, 5, 3, 6, 5, 2, 1, 5, 2, 5, 1, 3, 1, 2, 5
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OFFSET

1,1


REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

T. D. Noe and Christian N. K. Anderson, Table of n, a(n) for n = 1..10000 (first 1000 terms are from T. D. Noe)
Christian N. K. Anderson, n, the fixed point, a(n), and the trajectories for n = 1..10000.
M. Lal, Iterates of a numbertheoretic function, Math. Comp., 23 (1969), 181183.
Eric Weisstein's World of Mathematics, Sum of Prime Factors


EXAMPLE

20 > 2+2+5 = 9 > 3+3 = 6 > 2+3 = 5, so a(20) = length of sequence {20,9,6,5} = 4.


MAPLE

with(numtheory): P:=proc(q) local a, b, j, k, n; print(2);
for n from 2 to q do a:=n; b:=a; k:=1; while not isprime(a) do k:=k+1;
a:=ifactors(a)[2]; a:=add(a[j][1]*a[j][2], j=1..nops(a)); if a=b then k:=k1; break;
else b:=a; fi; od; print(k); od; end: P(10^4); # Paolo P. Lava, Apr 24 2015


MATHEMATICA

spf[n_] := Times @@@ FactorInteger[n] // Total; a[1] = 2; a[n_] := Length[ FixedPointList[spf, n]]  1; Array[a, 105] (* JeanFrançois Alcover, Feb 09 2018 *)


CROSSREFS

Cf. A001414 (sum of prime factors of n), A029908 (fixed point that is reached).
Sequence in context: A287917 A029434 A156281 * A157047 A059342 A062831
Adjacent sequences: A002214 A002215 A002216 * A002218 A002219 A002220


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms and better description from Reinhard Zumkeller, Apr 08 2003
Incorrect comment removed by Harvey P. Dale, Aug 16 2011


STATUS

approved



