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Numbers x such that x = concatenate(a, b) and phi(a) + phi(b) = sigma(x) - x.
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%I #11 Feb 05 2015 07:34:23

%S 49,169,289,611,1751,2171,2231,7921,10751,11479,23153,24367,38551,

%T 38809,49901,99101,116303,143351,229441,268151,271441,306181,357101,

%U 1030301,2014751,2078663

%N Numbers x such that x = concatenate(a, b) and phi(a) + phi(b) = sigma(x) - x.

%e 49 = concat(4,9); phi(4) = 2, phi(9) = 6, sigma(49) = 57; 2 + 6 = 8 = 57 - 49.

%e 169 = concat(16,9); phi(16) = 8, phi(9) = 6, sigma(169) = 183; 8 + 6 = 14 = 183-169.

%p with(numtheory); P:=proc(q) local a, b, i, n; for n from 1 to q do

%p for i from 1 to ilog10(n) do a:=trunc(n/10^i); b:=n-a*10^i;

%p if phi(a)+phi(b)=sigma(n)-n then print(n); break;

%p fi; od; od; end: P(10^9);

%Y Cf. A000010, A000203, A001065, A249065.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Feb 03 2015