A373515 - OEIS

%I #17 Jun 12 2024 17:23:33

%S 2,6,18,30,54,90,150,162,210,270,450,486,630,750,810,1050,1350,1458,

%T 1470,1890,2250,2310,2430,3150,3750,4050,4374,4410,5250,5670,6750,

%U 6930,7290,7350,9450,10290,11250,11550,12150,13122,13230,15750,16170,17010,18750,20250

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

%C 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.

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

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

%H Michael De Vlieger, <a href="/A373515/b373515.txt">Table of n, a(n) for n = 1..10000</a>

%e 6 is a term because 2|6 but 4!|6 and rad(6) = 6 = A002110(2) is a primorial number.

%e A primorial number m > 1 is a term since m is squarefree and == 2 (mod 4).

%t Select[Range[2, 25000, 4], Or[# == {2}, Union@ Differences@ PrimePi[#] == {1}] &@

%t FactorInteger[#][[All, 1]] &] (* _Michael De Vlieger_, Jun 08 2024 *)

%o (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

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

%K nonn

%O 1,1

%A _David James Sycamore_, Jun 07 2024