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

1,1

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

Links

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

Example

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).

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A324541 A351875 A197168 * A288815 A277200 A277324

Adjacent sequences: A373512 A373513 A373514 * A373516 A373517 A373518

Keyword

nonn

Author

David James Sycamore, Jun 07 2024

Status

approved