A272403 - OEIS

%I #9 Apr 29 2016 17:34:34

%S 13,17,31,71,103,107,113,131,137,167,173,179,191,197,311,431,701,971,

%T 1013,1019,1031,1061,1091,1097,1103,1109,1151,1163,1181,1193,1219,

%U 1223,1229,1277,1283,1301,1307,1339,1367,1373,1409,1433,1439,1487,1499,1511,1523

%N Numbers n = concat(x,y) such that (x - phi(x)) + (y - phi(y)) = n - phi(n), where n - phi(n) is the Euler cototient function of n.

%C Essentially primes. Only 58 squarefree composite in the first 10000 terms: 1219, 1339, 2869, 3743, 4427, 9707, 11569, 14269, 16105, 17125, 18733, 19375, 22927, 74069, 106159, 107629, 115069, 134959, 137533, 137843, 142417, 146207, 147943, 150421, 156857, 158899, 165625, 170033, 183595, 184375, 194627, 220417, 226417, 243293, 280873, 284371, 325067, 345827, 425261, 740821, 765403, 794837, 857257, 908647, 914231, 1005673, 1007509, 1037749, 1043527, 1188211, 1188919, 1296497, 1416019, 1428773, 1527167, 1528913, 1587227, 15906225.

%H Paolo P. Lava, <a href="/A272403/b272403.txt">Table of n, a(n) for n = 1..10000</a>

%e 137 - phi(137) = (1 - phi(1)) + (37 - phi(37)) = 1;

%e 1219 - phi(1219) = (1- phi(1)) + (219 - phi(219)) = 75;

%e 4427- phi(4427) = (442 - phi(442)) + (7- phi(7)) = 251.

%p with(numtheory): P:=proc(q) local x,y,k,n; for n from 1 to q do

%p for k from 1 to ilog10(n) do x:=n mod 10^k; y:=trunc(n/10^k);

%p if (x-phi(x))+(y-phi(y))=n-phi(n) then print(n); break; fi;

%p od; od; end: P(10^6);

%t Select[Range@ 1600, Function[m, AnyTrue[Map[FromDigits /@ TakeDrop[IntegerDigits@ m, #] &, Range[IntegerLength@ m - 1]], Total@ Map[# - EulerPhi@ # &, #] == m - EulerPhi@ m &]]] (* _Michael De Vlieger_, Apr 29 2016, Version 10.2 *)

%Y Cf. A000040, A051953, A272157.

%K nonn,base,easy

%O 1,1

%A _Paolo P. Lava_, Apr 29 2016