A274461 Least common multiple of first n proper prime powers.

1, 4, 8, 72, 144, 3600, 10800, 21600, 1058400, 2116800, 6350400, 768398400, 3841992000, 7683984000, 1298593296000, 3895779888000, 7791559776000, 2251760775264000, 15762325426848000, 5690199479092128000, 11380398958184256000, 6020231048879471424000, 30101155244397357120000, 90303465733192071360000

Offset: 0

Author

Franklin T. Adams-Watters, Jun 23 2016

Keywords

• nonn

Comments

Squares in this sequence include a(0)=1^2, a(1)=2^2, a(4)=12^2, a(5)=60^2, a(10)=2520^2, and a(11)=27720^2. Are there any more?

All terms in this sequence are powerful numbers (A001694).

Crossrefs

Cf. A051451, A246547, A001694.

Programs

Mathematica

t = Join[{1}, Select[Range@ 1000, Min@ FactorInteger[#][[All, 2]] > 1 &]]; Union@ Table[LCM @@ t[[1 ;; n]], {n, 45}] (* Michael De Vlieger, Jun 24 2016, after Harvey P. Dale at A001694 *)

PARI

alist(n)=my(pp=0,x=1);vector(n,k,while(isprimepower(pp++)<2&&pp!=1,0); x=lcm(x, pp))