cp's OEIS Frontend

A369020 Numbers k such that k and k+1 have the same maximal exponent in their prime factorization.

%I A369020 #11 Sep 11 2024 13:39:42
%S A369020 2,5,6,10,13,14,21,22,29,30,33,34,37,38,41,42,44,46,49,57,58,61,65,66,
%T A369020 69,70,73,75,77,78,80,82,85,86,93,94,98,99,101,102,105,106,109,110,
%U A369020 113,114,116,118,122,129,130,133,135,137,138,141,142,145,147,154,157
%N A369020 Numbers k such that k and k+1 have the same maximal exponent in their prime factorization.
%C A369020 Differs from A358817 by having the terms 99, 165, 166, ..., which are not in A358817, and not having the terms 1, 440, 1331, 1575, ..., which are in A358817.
%C A369020 Numbers k such that A051903(k) = A051903(k+1).
%C A369020 If k is a term then k*(k+1) is a term of A362605.
%C A369020 The asymptotic density of this sequence is d(2) + Sum_{k>=2} (d(k) + d(k+1) - 2 * d2(k)) = 0.36939178586283962461..., where d(k) = Product_{p prime} (1 - 2/p^k) and d2(k) = Product_{p prime} (1 - 1/p^k - 1/p^(k+1)).
%H A369020 Amiram Eldar, <a href="/A369020/b369020.txt">Table of n, a(n) for n = 1..10000</a>
%t A369020 emax[n_] := emax[n] = Max[FactorInteger[n][[;; , 2]]]; emax[1] = 0; Select[Range[200], emax[#] == emax[# + 1] &]
%o A369020 (PARI) emax(n) = if(n == 1, 0, vecmax(factor(n)[, 2]));
%o A369020 lista(kmax) = {my(e1 = 0, e2); for(k = 2, kmax, e2 = emax(k); if(e1 == e2, print1(k-1, ", ")); e1 = e2);}
%Y A369020 Cf. A051903, A358817, A362605, A369022.
%Y A369020 Subsequences: A007674, A071318, A369021.
%K A369020 nonn,easy
%O A369020 1,1
%A A369020 _Amiram Eldar_, Jan 12 2024