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A048107
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Numbers k such that the number of unitary divisors of k (A034444) is larger than the number of non-unitary divisors of k (A048105).
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12
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1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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n = 420 = 2*2*3*5*7, 4 distinct prime factors, 24 divisors of which 16 are unitary and 8 are not; ud(n) > nud(n) and 2^(4+1) = 32 is larger than d, the number of divisors.
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MATHEMATICA
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Select[Range[500], 2^(1 + PrimeNu[#]) > DivisorSigma[0, #] &] (* G. C. Greubel, May 05 2017 *)
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PROG
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(PARI) is(n)=my(f=factor(n)[, 2], t); for(i=1, #f, if(f[i]>1, if(t||f[i]>2, return(0), t=1))); 1 \\ Charles R Greathouse IV, Sep 17 2015
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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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