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A291320
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Numbers k such that uphi(k) is equal to the sum of the proper unitary divisors of k.
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0
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OFFSET
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1,1
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COMMENTS
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Or numbers k such that usigma(k) - k = uphi(k) where usigma(k) = A034448(k) and uphi(k) = A047994(k).
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LINKS
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EXAMPLE
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600 = 2^3*3*5^2 is a term because usigma(600) - uphi(600) = (2^3+1)*(3+1)*(5^2+1) - (2^3-1)*(3-1)*(5^2-1) = 600.
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MATHEMATICA
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ok[n_] := Block[{p = Power @@@ FactorInteger[n]}, Times @@ (p + 1) == n + Times @@ (p - 1)]; Select[Range[2, 10^6], ok] (* Giovanni Resta, Aug 22 2017 *)
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PROG
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(PARI) usigma(n) = sumdivmult(n, d, if(gcd(d, n/d)==1, d));
uphi(n) = my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1);
isok(n) = usigma(n)-uphi(n)==n;
(PARI) list(lim)=my(v=List()); forfactored(n=2, lim\1, if(sumdivmult(n, d, if(gcd(d, n[1]/d)==1, d))-prod(i=1, #n[2]~, n[2][i, 1]^n[2][i, 2]-1)==n[1], listput(v, n[1]))); Vec(v) \\ Charles R Greathouse IV, Aug 22 2017
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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