cp's OEIS Frontend

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.

%I A271384 #10 Apr 09 2016 16:39:55
%S A271384 3,14,20,28,44,92,112,224,266,260,404,380,476,552,558,696,860,984,846,
%T A271384 1062,1388,1128,1278,1752,1494,1422,2034,1926,1704,1992,2358,2466,
%U A271384 2712,2424,2718,3222,3006,3258,4924,3288,3582,4296,3798,4008,4518,5688,5094,5352
%N 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.
%H A271384 Paolo P. Lava, <a href="/A271384/b271384.txt">Table of n, a(n) for n = 1..50</a>
%e A271384 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;
%e A271384 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.
%p A271384 with(numtheory): P:=proc(q) local a,h,k,n; for h from 1 to q do
%p A271384 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;
%p A271384 if a=h then print(n); break; fi; od; od; end: P(10^9);
%t A271384 Table[SelectFirst[Range[10 + 5 n^2], Function[k, With[{e = EulerPhi@ k},
%t A271384 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 *)
%Y A271384 Cf. A000005, A211224, A271382.
%K A271384 nonn,easy
%O A271384 1,1
%A A271384 _Paolo P. Lava_, Apr 06 2016