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A238230
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Numbers m such that if x = sigma(m)-phi(m)-tau(m)-m then m = sigma(x)-phi(x)-tau(x)-x.
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6
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198, 294, 16008, 22232, 150030, 195320, 200274, 3038720, 12190720, 124904790, 167179722, 347943288, 426853240, 528995656, 646186568, 3588779502, 4798752860, 5376246738, 5898361924, 158380893880, 189740533470, 196271084296, 240458641570, 375653406648
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OFFSET
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1,1
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COMMENTS
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All numbers of the form 2^k*5*p, where p = (7*2^k-2*k-5)/3 is prime, are fixed points and thus terms. This happens for k = 9, 10, 124, 352, 1468, 3339, 4365,... - Giovanni Resta, Mar 26 2014
The fixed points (terms with x = m) are 198, 294, 195320, 3038720, 12190720, ... - Amiram Eldar, Mar 31 2019
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LINKS
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EXAMPLE
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Fixed points: 198, 294, 195320,...
sigma(16008) = 43200, phi(16008) = 4928, tau(16008) = 32 and 43200 - 4928 - 32- 16008 = 22232.
sigma(22232) = 47760, phi(22232) = 9504, tau(22232) = 16 and 47760 - 9504 - 16 - 22232 = 16008.
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MAPLE
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with(numtheory); P:=proc(q)local a, n;
for n from 1 to q do a:=sigma(n)-phi(n)-tau(n)-n;
if a>0 and sigma(a)-phi(a)-tau(a)-a=n then print(n);
fi; od; end: P(10^6);
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MATHEMATICA
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f[n_] := If[n > 0, DivisorSigma[1, n] - EulerPhi[n] - DivisorSigma[0, n] - n, 0]; s={}; Do[ If[f[f[n]] == n, AppendTo[s, n]], {n, 1, 200000}]; s (* Amiram Eldar, Mar 31 2019 *)
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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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