A238228 -id:A238228 - cp's OEIS frontend

A238227 Numbers n such that if x=sigma(n)-tau(n)-n then n=sigma(x)-tau(x)-x.

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

Paolo P. Lava, Feb 20 2014

nonn

If the second term (4) is not considered, A056075 is almost a subset of this sequence: it lists the fixed points of the transform n -> sigma(n)-tau(n)-n.

			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.

Amiram Eldar, Table of n, a(n) for n = 1..1001 (terms 1..50 from Paolo P. Lava)

Cf. A000005, A000203, A056075, A238225, A238226, A238228, A238229, A238230.

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);

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

Paolo P. Lava, Feb 20 2014

nonn

The fixed points (terms with x = n) are 2, 4, 20, 66, 342, 41922, 10983114, ... - Amiram Eldar, Mar 31 2019

			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.

Kevin P. Thompson, Table of n, a(n) for n = 1..38

Cf. A000005, A000010, A000203.

Cf. A238225, A238226, A238227, A238228, A238230.

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 *)

a(11)-a(29) from Amiram Eldar, Mar 31 2019

a(30) from Giovanni Resta, Apr 04 2019

cp's OEIS Frontend

A238227 Numbers n such that if x=sigma(n)-tau(n)-n then n=sigma(x)-tau(x)-x.

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