A373515 Numbers k, divisible by 2 but not by 4, such that rad(k) is primorial.

2, 6, 18, 30, 54, 90, 150, 162, 210, 270, 450, 486, 630, 750, 810, 1050, 1350, 1458, 1470, 1890, 2250, 2310, 2430, 3150, 3750, 4050, 4374, 4410, 5250, 5670, 6750, 6930, 7290, 7350, 9450, 10290, 11250, 11550, 12150, 13122, 13230, 15750, 16170, 17010, 18750, 20250

Offset: 1

Author

David James Sycamore, Jun 07 2024

Keywords

• nonn

Comments

Intersection of A055932 and A016825. In other words, numbers k congruent to 2 (mod 4) such that the squarefree kernel of k is a term in A002110. A term m in A055932 is in this sequence iff m/2 is an odd number.

If x, y are terms in this sequence then x*y is not. All primorial numbers >= 2 are terms.

For i >= 1, primorial A002110(i) is a term in this sequence, since primorials are squarefree. - Michael De Vlieger, Jun 08 2024

Examples

			6 is a term because 2|6 but 4!|6 and rad(6) = 6 = A002110(2) is a primorial number.
A primorial number m > 1 is a term since m is squarefree and == 2 (mod 4).
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A007947, A016825, A055932, A080404.

Programs

Mathematica

Select[Range[2, 25000, 4], Or[# == {2}, Union@ Differences@ PrimePi[#] == {1}] &@
FactorInteger[#][[All, 1]] &] (* Michael De Vlieger, Jun 08 2024 *)

PARI

lista(kmax) = {my(f); forstep(k = 2, kmax, 4, f = factor(k); if(primepi(f[#f~, 1]) == #f~, print1(k, ", ")));} \\ Amiram Eldar, Jun 08 2024