Composites Between Adjacent Primes

[Pfoertner, Hugo]

-----Original Message-----
From: Leroy Quet [mailto:qq-quet at mindspring.com] 
Sent: Wednesday, February 08, 2006 16:34
To: seqfan at ext.jussieu.fr
Subject: Composites Between Adjacent Primes
>The sequence where a(n) = (the highest prime dividing the product of the 
>composites between p(n) and p(n+1)) is not in the EIS, apparently.
>It starts, if I did not error,
>2,3,5,3,7,3,7,13,5,17,...

You did :-(

Should be:
http://www.research.att.com/projects/OEIS?Anum=A052248 
2,3,5,3,7,3,11,13,5,17,19,7,23,17,29,5,31,23,3,37,41,43,47,
....
Name: Greatest prime divisor of all composite numbers between p and next
prime.
Comments:  Or, largest of all prime factors of the numbers between prime(n)
and prime(n+1).
Author: njas

Leroy wrote:
>And the composites divisible by these primes form the sequence, whose 
>definition must be modified if there are more than one such composite for 
>any particular n,
>4,6,10,12,14,18,21,26,30,34,...

Should be: (not in OEIS)
4 6 10 12 14 18 22 26 30 34 38 42 46 51 58 60 62 69 72 74 82 86 94 99
102 106 108 111 122 129 134 138 146 150 155 158 166 172 178 180 183 192
194 198 206 218 226 228 232 237 240 249 254 262 267 270 274 278 282 291
302 309 312 314 326 334 346 348 351 358 362 371 376 382 386 394 398 404

----------------------------------------------

If we divide each term by the corresponding terms of A052248, we get

2 2 2 4 2 6 2 2 6 2 2 6 2 3 2 12 2 3 24 2 2 2 2 9 6 2 3 3 2 3 2 6 2 30 5
2 2 4 2 36 3 64 2 18 2 2 2 12 8 3 48 3 2 2 3 54 2 2 6 3 2 3 24 2 2 2 2 12
27 2 2 7 8 2 2 2 2 4 3 60 2 144 4 26 2 2 2 42 2 2 2 3 6 2 4 2 18 2 2 2 2
2 30 3 2 3 3 120 4 10 2 6 2 2 6 15 4 5 60

I don't know if this is of any use.
"Composite between two primes with biggest prime factor, divided by this
factor"
Is there a better definition?

Hugo