|
Search: id:A075860
|
|
|
| A075860 |
|
Starting with n, repeatedly sum prime divisors (without multiplicity) until reaching 0 or a fixed point. |
|
+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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
For n>1, the sequence reaches a fixed point, which is prime.
|
|
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.
|
|
MATHEMATICA
|
f[n_] := Module[{a}, a = n; While[ !PrimeQ[a], a = Apply[Plus, Transpose[FactorInteger[a]][[1]]]]; a]; Table[f[i], {i, 2, 100}]
|
|
CROSSREFS
|
A008472(n) is sum of prime divisors of n. Cf. A029908.
Sequence in context: A141346 A095402 A086294 this_sequence A008472 A123528 A074036
Adjacent sequences: A075857 A075858 A075859 this_sequence A075861 A075862 A075863
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Oct 15 2002
|
|
EXTENSIONS
|
Better description from Labos E. (labos(AT)ana.sote.hu), Apr 09 2003
|
|
|
Search completed in 0.002 seconds
|
