A271384 Least k with precisely n partitions k = x + y satisfying phi(k) = phi(x) + phi(y), where phi(k) is the Euler totient function of k.

3, 14, 20, 28, 44, 92, 112, 224, 266, 260, 404, 380, 476, 552, 558, 696, 860, 984, 846, 1062, 1388, 1128, 1278, 1752, 1494, 1422, 2034, 1926, 1704, 1992, 2358, 2466, 2712, 2424, 2718, 3222, 3006, 3258, 4924, 3288, 3582, 4296, 3798, 4008, 4518, 5688, 5094, 5352

Offset: 1

Author

Paolo P. Lava, Apr 06 2016

Keywords

• nonn
• easy

Examples

			phi(28) = phi(6) + phi(22) = phi(8) + phi(20) = phi(12) + phi(16) = phi(14) + phi(14) = 12 and 28 is the least number with 4 partitions of two numbers with this property: therefore a(4) = 28;
phi(112) = phi(14) + phi(98) = phi(24) + phi(88) = phi(30) + phi(82) = phi(32) + phi(80) = phi(36) + phi(76) = phi(48) + phi(64) = phi(56) + phi(56) = 48 and 112 is the least number with 7 partitions of two numbers with this property: therefore a(7) = 112.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A000005, A211224, A271382.

Programs

Maple

with(numtheory): P:=proc(q) local a,h,k,n; for h from 1 to q do
for n from 2*h to q do a:=0; for k from 1 to trunc(n/2) do if phi(n)=phi(k)+phi(n-k) then a:=a+1; fi; od;
if a=h then print(n); break; fi; od; od; end: P(10^9);

Mathematica

Table[SelectFirst[Range[10 + 5 n^2], Function[k, With[{e = EulerPhi@ k},
Count[Transpose@ {Range[k - 1, Ceiling[k/2], -1], Range@ Floor[k/2]}, x_ /; Total@ EulerPhi@ x == e] == n]]], {n, 25}] (* Michael De Vlieger, Apr 06 2016, Version 10 *)