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
Keywords
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.
Programs
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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);
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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
Comments