A365899 - OEIS

%I #12 Oct 01 2023 07:26:22

%S 2935,5446,5910,9093,11068,15713,15795,18829,19984,23669,25794,26386,

%T 33619,36370,36498,41560,41779,46911,48184,48231,48604,50349,50835,

%U 53082,53253,53760,54758,56524,58144,58836,59600,60390,60533,63181,64979,65226,65867,66449

%N Numbers k such that A073734(k) is neither squarefree nor a prime power.

%C Subset of A073735.

%C A073734(a(n)) = GCD(A064413(a(n)-1), A064413(a(n))) is in A126706.

%H Michael De Vlieger, <a href="/A365899/b365899.txt">Table of n, a(n) for n = 1..10000</a>

%H Michael De Vlieger, <a href="/A365899/a365899.txt">Mathematica code</a> for this sequence, based on Lagarias-Rains-Sloane 2002 paper, pages 4-5.

%H J. C. Lagarias, E. M. Rains and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0204011">The EKG sequence</a>, Exper. Math. 11 (2002), 437-446; arXiv:math/0204011 [math.NT], 2002.

%H <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>

%e Table of first terms and how they relate to b(n) = A073735(n) and EKG(n) = A064413(n).

%e    n   m=a(n)  b(m)          EKG(m-1)  EKG(m)

%e   -------------------------------------------

%e    1    2935    20 = 2*2*5      3080    3060

%e    2    5446    20              5740    5660

%e    3    5910    20              6180    6140

%e    4    9093    20              9460    9440

%e    5   11068    12 = 2*2*3     11484   11472

%e    6   15713    52 = 2*2*13    16328   16276

%e    7   15795    12             16368   16356

%e    8   18829    36 = 2*2*3*3   19548   19476

%e    9   19984    63 = 3*3*7     20727   20664

%e   10   23669   116 = 2*2*29    24592   24476

%e   11   25794    56 = 2*2*2*7   26712   26656

%e   12   26386    68 = 2*2*17    27472   27268

%e   ...

%e   30   58836    18 = 2*3*3     60786   60778

%e   ...

%Y Cf. A064413, A073734, A073735, A126706.

%K nonn

%O 1,1

%A _Michael De Vlieger_, Sep 28 2023