[seqfan] Add to an integer its distinct factors and loop

[Eric Angelini]

Hello SeqFans,

"Add to an integer N its distinct factors and loop"
[is this old hat?]

Example (taken from this nice page by Richard Mathar):
http://www.strw.leidenuniv.nl/~mathar/progs/A045778.txt

(1) start with N = 6
(2) factorization of 6 into distinct factors: 6 = 2*3
(3) add said factors to 6: 6+2+3 = 11
(4) factorization of 11 into distinct factors: END

Another try:

(1) start with N = 8
(2) factorization of 8 into distinct factors: 8 = 2*4
(3) add said factors to 8: 8+2+4 = 14
(4) factorization of 14 into distinct factors: 14 = 2*7
(5) add said factors to 14: 14+2+7 = 23
(4) factorization of 23 into distinct factors: END

Thus we have:

 6-->2*3--->11-->END
 8-->2*4--->14-->2*7--->23-->END
10-->2*5--->17-->END
12-->2*6--->20-->2*10-->32-->2*16-->50-->2*25-->77-->7*11-->95--->...
12-->2*6--->20-->2*10-->32-->2*16-->50-->5*10-->65-->5*13-->83--->END
12-->2*6--->20-->2*10-->32-->4*8--->44-->2*22-->68-->2*34-->104-->...
12-->2*6--->20-->2*10-->32-->4*8--->44-->2*22-->68-->4*17-->89--->END
12-->2*6--->20-->2*10-->32-->4*8--->44-->4*11-->59-->END
12-->2*6--->20-->4*5--->29-->END
12-->3*4--->19-->END
15-->3*5--->23-->END
16-->2*8--->26-->2*13-->41-->END
18-->2*9--->29-->END
18-->3*6--->27-->3*9--->39-->3*13-->55-->5*11-->71-->END
21-->3*7--->31-->END
22-->2*11-->35-->5*7--->47-->END
24-->2*3*4->33-->3*11-->47-->END
24-->2*12-->38-->2*19-->59-->END
24-->3*8--->35-->5*7--->47-->END
24-->4*6--->34-->2*17-->53-->END
25-->5*5--->35-->5*7--->47-->END
28-->2*14-->44 (see 3rd '12' above)-->...
28-->4*7--->39 (see 2nd '18' above)-->END
...

Lots of ENDs!
What about exploring those "trees"? (attractors, flights,...)

Best,
É.