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A239801
Numbers k such that if x = sigma(k) - k then k = x - phi(x), where phi(k) is the Euler totient function.
1
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).
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
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