OFFSET
1,1
LINKS
Paolo P. Lava, Table of n, a(n) for n = 1..50
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Apr 06 2016
STATUS
approved