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A259629 "Near Primorial" numbers.

%I A259629 #15 Aug 11 2015 15:30:44
%S A259629 10,15,42,70,105,330,462,770,1155,2730,4290,6006,10010,15015,39270,
%T A259629 46410,72930,102102,170170,255255,570570,746130,881790,1385670,
%U A259629 1939938,3233230,4849845,11741730,13123110,17160990,20281170,31870410,44618574,74364290,111546435,281291010
%N A259629 "Near Primorial" numbers.
%C A259629 These are non-primorial (and nonprime) numbers missing just one prime factor relative to some primorial. The primorial numbers are given by A002110.
%C A259629 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 A259629 Chai Wah Wu, <a href="/A259629/b259629.txt">Table of n, a(n) for n = 1..1034</a>
%e A259629 42 is included because it has prime factors 2, 3, and 7, but not 5.
%e A259629 105 is included because it has prime factors 3, 5 and 7, but not 2.
%t A259629 ResultList = {}; primo = 6; Do[primo = primo * Prime[n];
%t A259629 Do[AppendTo[ResultList, primo/Prime[m]], {m, 1, n - 1}], {n, 3, 15}] ; Sort[ResultList]
%o A259629 (Python)
%o A259629 from __future__ import division
%o A259629 from sympy import nextprime
%o A259629 A259629_list, plist, p = [10, 15], [10, 15], 5
%o A259629 for _ in range(50):
%o A259629     r = nextprime(p)
%o A259629     plist = [plist[-1]*2*r//p]+[d*r for d in plist]
%o A259629     A259629_list.extend(plist)
%o A259629     p = r # _Chai Wah Wu_, Aug 11 2015
%Y A259629 Cf. A002110.
%K A259629 nonn
%O A259629 1,1
%A A259629 _Richard R. Forberg_, Jul 01 2015