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%I #8 Jul 08 2021 06:48:06
%S 1,9,58,61,73,80,82,1224,1368,3075,3720,5328,22112,45890,145132,
%T 145138,269843,377739,399281,622515,744768,1280073,1280437,1280441,
%U 1281165,1281190,1281241,2961840,33275384,54025424,54161775,70695344,91136415,922135875,922141772
%N Numbers k such that A064839(k) = A064839(k+1).
%C The corresponding values of A064839 are 1, 2, 17, 18, 21, 2, 23, 10, 12, 278, 18, 21, 150, 2842, 13434, 13435, 13547, 3654, 33805, 55229, 150, 265608, 265682, 265683, 265832, 265837, 265849, 268, 773172, 308093, 308810, 395158, 540683, 24172493, 24172646, ...
%C Are there numbers k such that A064839(k) = A064839(k+1) = A064839(k+2)?
%e 9 is a term since 9 = 3^2 = A001248(2) is the second square of a prime, and 9 + 1 = 10 = 2 * 5 = A006881(2) is the second squarefree semiprime.
%e 58 is a term since 58 = 2*29 = A001248(17) is the 17th squarefree semiprime, and 58 + 1 = 59 = A000040(17) is the 17th prime.
%t lpsv = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]; lps[n_] := Module[{s = Sort[FactorInteger[n][[;; , 2]]], m}, m = Length[s]; Product[Prime[i]^s[[m - i + 1]], {i, 1, m}]]; n = 100; mx = lpsv[[n]]; c = Table[0, {n}]; v1 = 1; s = {}; Do[lps1 = lps[k]; p = Position[lpsv, lps1][[1, 1]]; c[[p]]++; v2 = c[[p]]; If[v1 == v2, AppendTo[s, k - 1]]; v1 = v2, {k, 2, mx}]; s
%Y Cf. A025487, A064839.
%Y Cf. A001248, A006881.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jul 07 2021
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