A238225 Composite numbers n such that if x = sigma(n)-phi(n)-n then n = sigma(x)-phi(x)-x.

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

Author

Paolo P. Lava, Feb 20 2014

Keywords

• nonn

Comments

A088826 is a subset of this sequence: it lists the fixed points of the transform n -> sigma(n)-phi(n)-n.

a(29) > 10^9. - Michel Marcus, Mar 06 2014

Examples

			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.
		

Crossrefs

Cf. A000010, A000203, A088826, A238226-A238230.

Programs

Maple

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);

PARI

isok(n) = !isprime(n) && ((x = (sigma(n) - eulerphi(n) - n)) > 0) && (n == (sigma(x) - eulerphi(x) - x)); \\ Michel Marcus, Mar 06 2014

Extensions

a(8)-a(28) from Michel Marcus, Mar 06 2014