A273801 Numbers n for which n = (x - phi(x)) * (y - phi(y)), where n = x + y and x - phi(x) is the Euler cototient function of x.

16, 24, 32, 48, 56, 72, 80, 96, 120, 128, 152, 168, 176, 192, 216, 240, 248, 272, 288, 296, 320, 336, 360, 392, 408, 416, 432, 440, 456, 512, 528, 552, 560, 600, 608, 632, 656, 672, 696, 720, 728, 768, 776, 792, 800, 848, 896, 912, 920, 936, 960, 968, 1008, 1032

Offset

1,1

Links

Paolo P. Lava, Table of n, a(n) for n = 1..200

Formula

a(n) = 4*(prime(n+1) + 1). - Paolo P. Lava, Sep 06 2017

Example

16 = 4 + 12 = (4 - phi(4)) * (12 - phi(12)) = 2 * 8 = 16 and also
16 = 8 + 8 = (8 - phi(8)) * (8 - phi(8)) = 4 * 4 = 16;
24 = 4 + 20 = (4 - phi(4)) * (20 - phi(20)) = 2 * 12 = 24.

Maple

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

Mathematica

Select[Range@ 1032, Function[n, Length@ Select[Times @@ Map[(# - EulerPhi@ #) &, {#, n - #}] & /@ Range[0, Floor[n/2]], # == n &] > 0]] (* Michael De Vlieger, Jun 01 2016 *)

Crossrefs

Cf. A051953, A273800.

Sequence in context: A253782 A247065 A082803 * A163284 A100316 A206260

Adjacent sequences: A273798 A273799 A273800 * A273802 A273803 A273804

Keyword

nonn

Author

Paolo P. Lava, May 31 2016

Status

approved