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

1,1

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

Cf. A000005, A211224, A271382.

Sequence in context: A121226 A063633 A108933 * A108420 A015639 A019000

Adjacent sequences: A271381 A271382 A271383 * A271385 A271386 A271387

Keyword

nonn,easy

Author

Paolo P. Lava, Apr 06 2016

Status

approved