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)

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

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 number-theoretic function, Math. Comp., 23 (1969), 181-183.

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.

Mathematica

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

Crossrefs

Cf. A001414 (sum of prime factors of n), A029908 (fixed point that is reached).

Sequence in context: A029434 A358192 A156281 * A344173 A157047 A059342

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