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A365899 Numbers k such that A073734(k) is neither squarefree nor a prime power.

%I A365899 #12 Oct 01 2023 07:26:22
%S A365899 2935,5446,5910,9093,11068,15713,15795,18829,19984,23669,25794,26386,
%T A365899 33619,36370,36498,41560,41779,46911,48184,48231,48604,50349,50835,
%U A365899 53082,53253,53760,54758,56524,58144,58836,59600,60390,60533,63181,64979,65226,65867,66449
%N A365899 Numbers k such that A073734(k) is neither squarefree nor a prime power.
%C A365899 Subset of A073735.
%C A365899 A073734(a(n)) = GCD(A064413(a(n)-1), A064413(a(n))) is in A126706.
%H A365899 Michael De Vlieger, <a href="/A365899/b365899.txt">Table of n, a(n) for n = 1..10000</a>
%H A365899 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 A365899 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 A365899 <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>
%e A365899 Table of first terms and how they relate to b(n) = A073735(n) and EKG(n) = A064413(n).
%e A365899    n   m=a(n)  b(m)          EKG(m-1)  EKG(m)
%e A365899   -------------------------------------------
%e A365899    1    2935    20 = 2*2*5      3080    3060
%e A365899    2    5446    20              5740    5660
%e A365899    3    5910    20              6180    6140
%e A365899    4    9093    20              9460    9440
%e A365899    5   11068    12 = 2*2*3     11484   11472
%e A365899    6   15713    52 = 2*2*13    16328   16276
%e A365899    7   15795    12             16368   16356
%e A365899    8   18829    36 = 2*2*3*3   19548   19476
%e A365899    9   19984    63 = 3*3*7     20727   20664
%e A365899   10   23669   116 = 2*2*29    24592   24476
%e A365899   11   25794    56 = 2*2*2*7   26712   26656
%e A365899   12   26386    68 = 2*2*17    27472   27268
%e A365899   ...
%e A365899   30   58836    18 = 2*3*3     60786   60778
%e A365899   ...
%Y A365899 Cf. A064413, A073734, A073735, A126706.
%K A365899 nonn
%O A365899 1,1
%A A365899 _Michael De Vlieger_, Sep 28 2023