A259629 "Near Primorial" numbers.

10, 15, 42, 70, 105, 330, 462, 770, 1155, 2730, 4290, 6006, 10010, 15015, 39270, 46410, 72930, 102102, 170170, 255255, 570570, 746130, 881790, 1385670, 1939938, 3233230, 4849845, 11741730, 13123110, 17160990, 20281170, 31870410, 44618574, 74364290, 111546435, 281291010

Offset: 1

Author

Richard R. Forberg, Jul 01 2015

Keywords

• nonn

Comments

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

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.

Examples

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1034

Crossrefs

Cf. A002110.

Programs

Mathematica

ResultList = {}; primo = 6; Do[primo = primo * Prime[n];
Do[AppendTo[ResultList, primo/Prime[m]], {m, 1, n - 1}], {n, 3, 15}] ; Sort[ResultList]

Python

from _future_ import division
from sympy import nextprime
A259629_list, plist, p = [10, 15], [10, 15], 5
for _ in range(50):
    r = nextprime(p)
    plist = [plist[-1]*2*r//p]+[d*r for d in plist]
    A259629_list.extend(plist)
    p = r # Chai Wah Wu, Aug 11 2015