cp's OEIS Frontend

A333052 Numbers m such that d(m) = d(m+1) and d(k) < d(m) for all k < m such that d(k) = d(k+1), where d(m) is the number of divisors of m (A000005).

%I A333052 #6 Mar 06 2020 22:40:13
%S A333052 2,14,44,104,735,2295,5264,5984,21735,201824,3341624,6481475,7316000,
%T A333052 49727600,103488384,205684479,349167104,391738599,1921172175,
%U A333052 6110171144,7616307699
%N A333052 Numbers m such that d(m) = d(m+1) and d(k) < d(m) for all k < m such that d(k) = d(k+1), where d(m) is the number of divisors of m (A000005).
%C A333052 The corresponding numbers of divisors are 2, 4, 6, 8, 12, 16, 20, 24, 32, 48, 64, 72, 96, 120, 128, 144, 160, 192, 240, 256, 288, ...
%e A333052 2 is a term since (2, 3) is the first pair of consecutive numbers with the same number of divisors: d(2) = d(3) = 2.
%e A333052 14 is a term since d(14) = d(15) = 4 > d(2) = 2.
%e A333052 44 is a term since d(44) = d(45) = 6 > d(14) = 4.
%t A333052 seq = {}; dmax = 0; d1 = 1; Do[If[d1 == (d2 = DivisorSigma[0, n]) && d1 > dmax, dmax = d1; AppendTo[seq, n-1]]; d1 = d2, {n, 2, 10^4}]; seq
%Y A333052 Cf. A000005, A002182, A005237, A175143.
%K A333052 nonn,more
%O A333052 1,1
%A A333052 _Amiram Eldar_, Mar 06 2020