A372666 Numbers of the form A002110(k)/prime(i); i = 2..k-1; sorted.

10, 42, 70, 330, 462, 770, 2730, 4290, 6006, 10010, 39270, 46410, 72930, 102102, 170170, 570570, 746130, 881790, 1385670, 1939938, 3233230, 11741730, 13123110, 17160990, 20281170, 31870410, 44618574, 74364290, 281291010, 340510170, 380570190, 497668710, 588153930

Offset: 1

Author

David James Sycamore, May 09 2024

Keywords

• nonn

Comments

In other words, "almost primorial numbers": those obtained from primorials (A002110) through division by one single prime which is greater than the least prime divisor and less that the greatest prime divisor of each primorial (results sorted by size). Same as A077011 constrained by exclusion of A002110(k)/prime(1) and A002110(k)/prime(k), so there are no primorial or half primorial terms. Each primorial A002110(k), k > 2, contributes k-2 terms to the sequence.

All terms are even squarefree numbers.

Subsequence of A077011 and A005117.

Examples

			Since k > 2, we start with A002110(3) = 2*3*5 = 30 and 3 is the only prime divisor of 30 which fits the definition so 30/3 = 10 is a(1).
A002110(6) = 2*3*5*7*11*13 = 30030 contributes four terms to the sequence, namely 30030/11 = 2730, 30030/7 = 4290, 30030/5 = 6006, and 30030/3 = 10010.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10153

Crossrefs

Cf. A000040, A002110, A005117, A077011.

Programs

Mathematica

Flatten@ Table[P = Product[Prime[i], {i, n}]; Array[P/Prime[n - #] &, n - 2], {n, 3, 10}] (* Michael De Vlieger, May 10 2024 *)

Extensions

More terms from Michael De Vlieger, May 10 2024