A239801 Numbers k such that if x = sigma(k) - k then k = x - phi(x), where phi(k) is the Euler totient function.

24, 30, 126, 150, 198, 276, 280, 294, 336, 1644, 3084, 3750, 5720, 13482, 47424, 211884, 11718750, 51028120, 75570560, 88590144, 260661280, 7435072458, 7440172542, 19408312640, 184390255062, 410770687360

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..26.

Example

sigma(276) = 672 and 672 - 276 = 396; phi(396) = 120 and 396 - 120 = 276.

Maple

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

Prog

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

Crossrefs

Cf. A000010, A000203, A239802.

Sequence in context: A349689 A348630 A067952 * A123200 A167307 A161378

Adjacent sequences: A239798 A239799 A239800 * A239802 A239803 A239804

Keyword

nonn,more

Author

Paolo P. Lava, Mar 27 2014

Extensions

a(17)-a(20) from Michel Marcus, Mar 28 2014

a(21)-a(24) from Kevin P. Thompson, Jan 14 2022

a(25) from Kevin P. Thompson, Apr 19 2022

a(26) from Kevin P. Thompson, Jun 13 2022

Status

approved