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

1,1

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.

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A002110.

Sequence in context: A078818 A194267 A261853 * A212794 A048061 A188651

Adjacent sequences: A259626 A259627 A259628 * A259630 A259631 A259632

Keyword

nonn

Author

Richard R. Forberg, Jul 01 2015

Status

approved