A295221 - OEIS

%I #13 Nov 22 2017 08:43:07

%S 156,190,224,286,352,416,544,578,608,736,928,992,1184,1312,1376,1504,

%T 1696,1888,1952,33555776,33557824,33558208,33558464,33558592,33559616,

%U 33560768,33560896,33562304,33562432,33563456,33564992,33567808,33568448,33568576,33569216

%N Numbers k such that 2*A243823(k) = k.

%C Observations:

%C 1. There is a large gap between a(19) and a(20).

%C 2. Products 2^5 * prime(i), with 3 <= i <= 17, are in the sequence.

%C 3. Products 2^6 * prime(j), with 43391 <= j <= 82025, are in the sequence.

%C 4. a(1) = 2^2 * 3 * 13, and terms 190, 286, and 578 are even, but do not follow the pattern of 2^h*p prime.

%H Michael De Vlieger, <a href="/A295221/b295221.txt">Table of n, a(n) for n = 1..2886</a> (terms <= 36000000).

%H Michael De Vlieger, <a href="/A295221/a295221.txt">Prime decomposition of terms in a(n).</a>

%e a(1) = 156 since 2 * (A010846(156) + A000010(156) - 1) = 2 * (31 + 48 - 1) = 2 * 78 = 156.

%t Select[Range@ 3000, Function[n, 2 (n - (Count[Range@ n, _?(PowerMod[n, Floor@ Log2@ n, #] == 0 &)] + EulerPhi[n] - 1)) == n]] (* _Michael De Vlieger_, Nov 17 2017 *)

%Y Cf. A000010, A010846, A243823, A272619.

%K nonn

%O 1,1

%A _Michael De Vlieger_, Nov 17 2017