

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



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
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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(nk) 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



