cp's OEIS Frontend

A376141 The maximum exponent in the prime factorization of the numbers k such that k and k+1 have the same maximum exponent in their prime factorization.

%I A376141 #7 Sep 12 2024 07:48:39
%S A376141 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,2,1,1,4,1,1,1,
%T A376141 1,1,2,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,3,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,
%U A376141 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A376141 The maximum exponent in the prime factorization of the numbers k such that k and k+1 have the same maximum exponent in their prime factorization.
%H A376141 Amiram Eldar, <a href="/A376141/b376141.txt">Table of n, a(n) for n = 1..10000</a>
%F A376141 a(n) = A051903(A369020(n)).
%F A376141 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (d(2) + Sum_{k>=2} k * (d(k) + d(k+1) - 2 * d2(k)))/d0 = 1.14396758638154735362..., where d(k) = Product_{p prime} (1 - 2/p^k), d2(k) = Product_{p prime} (1 - 1/p^k - 1/p^(k+1)), and d0 = 0.36939178586283962461... is the asymptotic density of A369020.
%t A376141 emax[n_] := Max[FactorInteger[n][[;; , 2]]]; emax[1] = 0; With[{t = Table[emax[n], {n, 1, 500}]}, t[[Position[Differences[t], 0] // Flatten]]]
%o A376141 (PARI) emax(n) = if(n == 1, 0, vecmax(factor(n)[, 2]));
%o A376141 lista(kmax) = {my(e1 = 0, e2); for(k = 2, kmax, e2 = emax(k); if(e1 == e2, print1(e1, ", ")); e1 = e2);}
%Y A376141 Cf. A051903, A369020.
%K A376141 nonn,easy
%O A376141 1,17
%A A376141 _Amiram Eldar_, Sep 11 2024