login
Composite numbers n such that if x = sigma(n)-phi(n)-n then n = sigma(x)-phi(x)-x.
6

%I #17 Mar 06 2014 06:31:56

%S 12,42,1242,2010,2358,57990,65802,1782198,1890738,2504920,2733880,

%T 3286128,4181968,6137440,7861200,8233134,11208018,15228688,21445340,

%U 24563812,33714690,38928126,185154858,207494658,221604534,247017798,341398422,366777018

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

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

%C a(29) > 10^9. - _Michel Marcus_, Mar 06 2014

%e Fixed points: 12, 42, 1242, 6137440, 1385119360, ...

%e sigma(2010) = 4896, phi(2010) = 528 and 4896 - 528 - 2010 = 2358.

%e sigma(2358) = 5148, phi(2358) = 780 and 5148 - 780 - 2358 = 2010.

%p with(numtheory); P:=proc(q)local a,n;

%p for n from 1 to q do a:=sigma(n)-phi(n)-n;

%p if a>0 and sigma(a)-phi(a)-a=n then print(n);

%p fi; od; end: P(10^6);

%o (PARI) isok(n) = !isprime(n) && ((x = (sigma(n) - eulerphi(n) - n)) > 0) && (n == (sigma(x) - eulerphi(x) - x)); \\ _Michel Marcus_, Mar 06 2014

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

%K nonn

%O 1,1

%A _Paolo P. Lava_, Feb 20 2014

%E a(8)-a(28) from _Michel Marcus_, Mar 06 2014