A369021 - OEIS

%I #7 Jan 12 2024 10:04:05

%S 5,13,21,29,33,37,41,57,65,69,77,85,93,98,101,105,109,113,129,137,141,

%T 157,165,177,181,185,193,201,209,213,217,221,229,237,253,257,265,281,

%U 285,301,309,317,321,329,345,353,357,365,381,389,393,397,401,409,417,429

%N Numbers k such that k, k+1 and k+2 have the same maximal exponent in their prime factorization.

%C Numbers k such that A051903(k) = A051903(k+1) = A051903(k+2).

%C The asymptotic density of this sequence is d(2,3) + Sum_{k>=2} (d(k+1,3) - d(k,3) + 3*d2(k,2,1) - 3*d2(k,1,2)) = 0.13122214221443994377..., where d(k,m) = Product_{p prime} (1 - m/p^k) and d2(k,m1,m2) = Product_{p prime} (1 - m1/p^k - m2/p^(k+1)).

%H Amiram Eldar, <a href="/A369021/b369021.txt">Table of n, a(n) for n = 1..10000</a>

%t emax[n_] := emax[n] = Max[FactorInteger[n][[;; , 2]]]; emax[1] = 0; Select[Range[200], emax[#] == emax[# + 1] == emax[#+2] &]

%o (PARI) emax(n) = if(n == 1, 0, vecmax(factor(n)[, 2]));

%o lista(kmax) = {my(e1 = 0, e2 = 0, e3); for(k = 3, kmax, e3 = emax(k); if(e1 == e2 && e2 == e3, print1(k-2, ", ")); e1 = e2; e2 = e3);}

%Y Cf. A051903, A369022.

%Y Subsequence of A369020.

%Y Subsequences: A007675, A071319.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Jan 12 2024