A377847 Powerful numbers that are divisible by the cube of a single prime.
8, 16, 27, 32, 64, 72, 81, 108, 125, 128, 144, 200, 243, 256, 288, 324, 343, 392, 400, 500, 512, 576, 625, 675, 729, 784, 800, 968, 972, 1024, 1125, 1152, 1323, 1331, 1352, 1372, 1568, 1600, 1800, 1936, 2025, 2048, 2187, 2197, 2304, 2312, 2401, 2500, 2700, 2704, 2888, 2916
Offset: 1
Links
Programs
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Mathematica
q[n_] := Module[{e = Sort[FactorInteger[n][[;; , 2]]]}, e[[-1]] > 2 && (Length[e] == 1 || e[[-2]] == 2)]; With[{max = 3000}, Select[Union@ Flatten@Table[i^2 * j^3, {j, 1, max^(1/3)}, {i, 1, Sqrt[max/j^3]}], q]] -
PARI
is(k) = if(k == 1, 0, my(e = vecsort(factor(k)[, 2])); e[1] > 1 && e[#e] > 2 && (#e == 1 || e[#e - 1] == 2));
Formula
Sum_{n>=1} 1/a(n) = (15/Pi^2) * Sum_{p prime} 1/((p-1)*(p^2+1)) = 0.40258439321745859629... .
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