A238225
Composite numbers n such that if x = sigma(n)-phi(n)-n then n = sigma(x)-phi(x)-x.
Original entry on oeis.org
12, 42, 1242, 2010, 2358, 57990, 65802, 1782198, 1890738, 2504920, 2733880, 3286128, 4181968, 6137440, 7861200, 8233134, 11208018, 15228688, 21445340, 24563812, 33714690, 38928126, 185154858, 207494658, 221604534, 247017798, 341398422, 366777018
Offset: 1
Fixed points: 12, 42, 1242, 6137440, 1385119360, ...
sigma(2010) = 4896, phi(2010) = 528 and 4896 - 528 - 2010 = 2358.
sigma(2358) = 5148, phi(2358) = 780 and 5148 - 780 - 2358 = 2010.
-
with(numtheory); P:=proc(q)local a,n;
for n from 1 to q do a:=sigma(n)-phi(n)-n;
if a>0 and sigma(a)-phi(a)-a=n then print(n);
fi; od; end: P(10^6);
-
isok(n) = !isprime(n) && ((x = (sigma(n) - eulerphi(n) - n)) > 0) && (n == (sigma(x) - eulerphi(x) - x)); \\ Michel Marcus, Mar 06 2014
A238227
Numbers n such that if x=sigma(n)-tau(n)-n then n=sigma(x)-tau(x)-x.
Original entry on oeis.org
1, 56, 66, 70, 992, 1012, 2260, 2516, 6042, 6902, 7192, 7210, 7232, 7750, 7912, 8178, 9086, 10792, 12198, 13706, 17272, 30592, 32778, 33352, 35032, 40166, 44034, 45010, 46670, 47710, 55374, 62296, 63688, 65570, 114256, 132916, 133892, 138244, 141236, 146804, 155572
Offset: 1
Fixed points: 56, 7192, 7232, 7912, 10792, ...
sigma(66) = 144, tau(66) = 8 and 144 - 8 - 66 = 70.
sigma(70) = 144, tau(70) = 8 and 144 - 8 - 70 = 66.
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.
-
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);
-
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 *)
Showing 1-3 of 3 results.
Comments