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A068317
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Numbers n such that n*tau(n) > omega(n)*prime(n) where tau(n) is the number of divisors of n and omega(n) the number of distinct prime factors of n.
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1
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1, 2, 3, 4, 8, 9, 16, 24, 27, 32, 36, 48, 64, 72, 96, 108, 128, 144, 160, 180, 192, 216, 240, 256, 288, 320, 324, 360, 384, 400, 432, 480, 504, 512, 540, 576, 600, 640, 648, 672, 720, 756, 768, 792, 800, 840, 864, 896, 900, 936, 960, 972, 1000, 1008, 1024
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OFFSET
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1,2
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COMMENTS
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There are very few odd terms in the sequence: 1, 3, 9, 27, 30375, 33075,...
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LINKS
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MATHEMATICA
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Select[Range[1040], #*DivisorSigma[0, #] > PrimeNu[#]*Prime[#] &] (* Ivan Neretin, Mar 16 2017 *)
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PROG
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(PARI) for(n=1, 1000, if(numdiv(n)*n>omega(n)*prime(n), print1(n, ", ")))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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