A238226 Numbers k such that if x = sigma(k) + tau(k) - k then k = sigma(x) + tau(x) - x.

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

Author

Paolo P. Lava, Feb 20 2014

Keywords

• nonn

Comments

A083874 is a subset of this sequence: it lists the fixed points of the transform n -> sigma(n)+tau(n)-n.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..900 (terms 1..50 from Paolo P. Lava)

Crossrefs

Cf. A000005, A000203, A083874, A238225, A238227-A238230.

Programs

Maple

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);

Mathematica

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 *)