A238226
Numbers k such that if x = sigma(k) + tau(k) - k then k = sigma(x) + tau(x) - x.
Original entry on oeis.org
1, 3, 14, 52, 130, 144, 184, 274, 300, 586, 656, 8648, 10434, 11470, 12008, 15774, 17034, 18802, 19270, 21032, 22088, 22184, 23288, 34688, 35394, 36872, 38744, 39790, 65324, 65392, 67628, 68476, 153868, 163676, 188468, 198628, 254526, 263890, 379026, 463390
Offset: 1
Fixed points: 1, 3, 14, 52, 130, 184, 656, 8648, 12008, 34688, ...
sigma(144) = 403, tau(144) = 15 and 403 + 15 - 144 = 274.
sigma(274) = 414, tau(274) = 4 and 414 + 4 - 274 = 144.
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with(numtheory); P:=proc(q)local a,n;
for n from 1 to q do a:=sigma(n)+tau(n)-n;
if sigma(a)+tau(a)-a=n then print(n);
fi; od; end: P(10^6);
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f[n_] := DivisorSigma[0, n] + DivisorSigma[1, n] - n; s={}; Do[m = f[n]; If[f[m] == n, AppendTo[s, n]], {n, 1, 500000}]; s (* Amiram Eldar, Jul 12 2019 *)
A238229
Numbers n such that if x = sigma(n)-phi(n)+tau(n)-n then n = sigma(x)-phi(x)+tau(x)-x.
Original entry on oeis.org
2, 4, 20, 66, 342, 34092, 40842, 41922, 46242, 55422, 207624, 259448, 533172, 547300, 571992, 667408, 1531032, 1786288, 10983114, 114013752, 133506680, 323277822, 347360860, 386144360, 387415458, 459603716, 476991704, 1443279992, 1539484232, 15537978552
Offset: 1
Fixed points: 2, 4, 20, 66, 342, 41922, ...
Amicable pairs: (34092, 40842), (46242, 55422), (207624, 259448), ...
sigma(34092) = 86268, phi(34092) = 11352, tau(34092) = 18 and 86268 - 11352 + 18 - 34092 = 40842.
sigma(40842) = 88530, phi(40842) = 13608, tau(40842) = 12 and 88530 - 13608 + 12 - 40842 = 34092.
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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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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, 60000}]; s (* Amiram Eldar, Mar 31 2019 *)
A238228
Numbers n such that if x=sigma(n)+phi(n)-tau(n)-n then n=sigma(x)+phi(x)-tau(x)-x.
Original entry on oeis.org
12, 14, 27, 125, 127
Offset: 1
Fixed points: 27,...
sigma(12) = 28, phi(12) = 4, tau(12) = 6 and 28 + 4 - 6 - 12 = 14.
sigma(14) = 24, phi(14) = 6, tau(14) = 4 and 24 + 6 - 4 - 14 = 12.
Showing 1-3 of 3 results.
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