A239802 - OEIS

A239802

Numbers n such that if x = n - phi(n) then n = sigma(x) - x, where phi(n) 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

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OFFSET

1,1

COMMENTS

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

LINKS

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);

PROG

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

CROSSREFS

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

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

STATUS

approved