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"Near Primorial" numbers.
2

%I #15 Aug 11 2015 15:30:44

%S 10,15,42,70,105,330,462,770,1155,2730,4290,6006,10010,15015,39270,

%T 46410,72930,102102,170170,255255,570570,746130,881790,1385670,

%U 1939938,3233230,4849845,11741730,13123110,17160990,20281170,31870410,44618574,74364290,111546435,281291010

%N "Near Primorial" numbers.

%C These are non-primorial (and nonprime) numbers missing just one prime factor relative to some primorial. The primorial numbers are given by A002110.

%C A002110 also contains a comment that references these "near primorial" numbers in the context of graphs of tallies on the values of the differences among all distinct pairs of odd prime numbers.

%H Chai Wah Wu, <a href="/A259629/b259629.txt">Table of n, a(n) for n = 1..1034</a>

%e 42 is included because it has prime factors 2, 3, and 7, but not 5.

%e 105 is included because it has prime factors 3, 5 and 7, but not 2.

%t ResultList = {}; primo = 6; Do[primo = primo * Prime[n];

%t Do[AppendTo[ResultList, primo/Prime[m]], {m, 1, n - 1}], {n, 3, 15}] ; Sort[ResultList]

%o (Python)

%o from __future__ import division

%o from sympy import nextprime

%o A259629_list, plist, p = [10, 15], [10, 15], 5

%o for _ in range(50):

%o r = nextprime(p)

%o plist = [plist[-1]*2*r//p]+[d*r for d in plist]

%o A259629_list.extend(plist)

%o p = r # _Chai Wah Wu_, Aug 11 2015

%Y Cf. A002110.

%K nonn

%O 1,1

%A _Richard R. Forberg_, Jul 01 2015