A295221 Numbers k such that 2*A243823(k) = k.

156, 190, 224, 286, 352, 416, 544, 578, 608, 736, 928, 992, 1184, 1312, 1376, 1504, 1696, 1888, 1952, 33555776, 33557824, 33558208, 33558464, 33558592, 33559616, 33560768, 33560896, 33562304, 33562432, 33563456, 33564992, 33567808, 33568448, 33568576, 33569216

Offset

1,1

Comments

Observations:

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

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

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

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.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..2886 (terms <= 36000000).

Michael De Vlieger, Prime decomposition of terms in a(n).

Example

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

Mathematica

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 *)

Crossrefs

Cf. A000010, A010846, A243823, A272619.

Sequence in context: A299170 A112818 A047635 * A052477 A166397 A065709

Adjacent sequences: A295218 A295219 A295220 * A295222 A295223 A295224

Keyword

nonn

Author

Michael De Vlieger, Nov 17 2017

Status

approved