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A320966
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Powerful numbers A001694 divisible by a cube > 1.
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3
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8, 16, 27, 32, 64, 72, 81, 108, 125, 128, 144, 200, 216, 243, 256, 288, 324, 343, 392, 400, 432, 500, 512, 576, 625, 648, 675, 729, 784, 800, 864, 968, 972, 1000, 1024, 1125, 1152, 1296, 1323, 1331, 1352, 1372, 1568, 1600, 1728, 1800, 1936, 1944, 2000, 2025, 2048, 2187, 2197, 2304, 2312, 2401, 2500
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OFFSET
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1,1
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COMMENTS
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Powerful numbers that are not squares of squarefree numbers. - Amiram Eldar, Jun 25 2022
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = zeta(2)*zeta(3)/zeta(6) - 15/Pi^2 = 0.4237786821... . - Amiram Eldar, Jun 25 2022
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MATHEMATICA
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Select[Range[2500], (m = MinMax[FactorInteger[#][[;; , 2]]])[[1]] > 1 && m[[2]] > 2 &] (* Amiram Eldar, Jun 25 2022 *)
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PROG
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isA046099(n)=n=factor(n)[, 2]; for(i=1, #n, if(n[i]>2, return(1))); 0
for (k=1, 2500, if(isA001694(k)&&isA046099(k), print1(k, ", ")))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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