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A374461 Numbers k such that k and k+1 are both nonsquarefree exponentially odd numbers (A374459).

%I A374461 #11 Jul 10 2024 09:37:44
%S A374461 135,296,343,351,375,512,999,1160,1375,1431,1592,1624,2079,2295,2375,
%T A374461 2456,2727,2943,3104,3159,3429,3591,3624,3752,3992,4023,4184,4616,
%U A374461 4832,4887,4913,5048,5144,5319,5480,5535,6183,6344,6375,6655,6858,7047,7263,7479,7624
%N A374461 Numbers k such that k and k+1 are both nonsquarefree exponentially odd numbers (A374459).
%C A374461 The numbers of terms that do not exceed 10^k, for k = 3, 4, ..., are 7, 59, 556, 5539, 55329, 553188, 5531116, 55311354, ... . Apparently, the asymptotic density of this sequence exists and equals 0.005531... .
%H A374461 Amiram Eldar, <a href="/A374461/b374461.txt">Table of n, a(n) for n = 1..10000</a>
%e A374461 135 is a term since both 135 = 3^3 * 5 and 136 = 2^3 * 17 are nonsquarefree exponentially odd numbers.
%t A374461 q[n_] := q[n] = Module[{e = FactorInteger[n][[;; , 2]]}, AllTrue[e, OddQ] && ! AllTrue[e, # == 1 &]]; Select[Range[10000], q[#] && q[# + 1] &]
%o A374461 (PARI) is1(k) = {my(e = factor(k)[, 2]); for(i = 1, #e, if(!(e[i] %2), return(0))); for(i = 1, #e, if(e[i] >1, return(1))); 0;}
%o A374461 lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}
%Y A374461 Intersection of A068781 and A367695.
%Y A374461 Subsequence of A268335 and A374459.
%K A374461 nonn
%O A374461 1,1
%A A374461 _Amiram Eldar_, Jul 09 2024