A254624 Numbers x such that x = concatenate(a, b) and phi(a) + phi(b) = sigma(x) - x.

49, 169, 289, 611, 1751, 2171, 2231, 7921, 10751, 11479, 23153, 24367, 38551, 38809, 49901, 99101, 116303, 143351, 229441, 268151, 271441, 306181, 357101, 1030301, 2014751, 2078663

Offset: 1

Author

Paolo P. Lava, Feb 03 2015

Keywords

• nonn
• base

Examples

			49 = concat(4,9); phi(4) = 2, phi(9) = 6, sigma(49) = 57; 2 + 6 = 8 = 57 - 49.
169 = concat(16,9); phi(16) = 8, phi(9) = 6, sigma(169) = 183; 8 + 6 = 14 = 183-169.
		

Crossrefs

Cf. A000010, A000203, A001065, A249065.

Programs

Maple

with(numtheory); P:=proc(q) local a, b, i, n; for n from 1 to q do
for i from 1 to ilog10(n) do a:=trunc(n/10^i); b:=n-a*10^i;
if phi(a)+phi(b)=sigma(n)-n then print(n); break;
fi; od; od; end: P(10^9);