A239802 Numbers k such that if x = k - phi(k) then k = sigma(x) - x, where phi(k) is the Euler totient function.

36, 42, 186, 222, 270, 390, 396, 440, 656, 2220, 4140, 5622, 9400, 20214, 94816, 282540, 17578122, 85046840, 125948800, 145805120, 434435360, 11152607958, 11160256626

Offset

1,1

Comments

Fixed points of the transform k -> sigma(k-phi(k)) - k + phi(k).

a(24) > 5*10^10, if it exists. - Amiram Eldar, Nov 21 2024

Links

Table of n, a(n) for n=1..23.

Example

phi(222) = 72 and 222 - 72 = 150; sigma(150) = 372 and 372 - 150 = 222.

Maple

with(numtheory); P:=proc(q) local n; k:=0;
for n from 1 to q do if 2*n=sigma(n-phi(n))+phi(n) then print(n);
fi; od; end: P(10^9);

Mathematica

q[k_] := Module[{e = EulerPhi[k]}, DivisorSigma[1, k - e] - k + e == k]; Select[Range[300000], q] (* Amiram Eldar, Nov 21 2024 *)

Prog

(PARI) isok(n) = (x = n - eulerphi(n)) && (n == sigma(x) - x); \\ Michel Marcus, Mar 28 2014

Crossrefs

Cf. A000010, A000203, A239801.

Sequence in context: A162526 A078299 A225028 * A266242 A274241 A062519

Adjacent sequences: A239799 A239800 A239801 * A239803 A239804 A239805

Keyword

nonn,more

Author

Paolo P. Lava, Mar 27 2014

Extensions

a(17)-a(21) from Michel Marcus, Mar 28 2014

a(22)-a(23) from Amiram Eldar, Nov 21 2024

Status

approved