A346072 - OEIS

%I #19 Jul 16 2021 01:34:49

%S 3,16,21,36,45,57,69,77,95,99,100,133,139,141,185,217,247,271,349,812,

%T 834,882,884,1012,1018,1078,1138,1198,1256,1404,1478,1936,1985,2263,

%U 2345,2381,2477,2489,2549,2583,2631,2847,2855,2857,2865,2887,2903,2947,2969,2977,3005,3011,3023,3028

%N Numbers m such that there exist positive integers i < m and j > m such that m = Sum_{k=i..m-1} tau(k) and m = Sum_{k=m+1..j} tau(k), where tau(k) = number of divisors of k = A000005(k).

%C The terms show a wavelike growth pattern as n increases. See the linked image.

%H Scott R. Shannon, <a href="/A346072/b346072.txt">Table of n, a(n) for n = 1..5000</a>.

%H Scott R. Shannon, <a href="/A346072/a346072.png">Image of the first 5000 terms</a>.

%e 3 is a term as tau(1) + tau(2) = 1 + 2 = 3, and tau(4) = 3.

%e 16 is a term as tau(12) + tau(13) + tau(14) + tau(15) = 6 + 2 + 4 + 4 = 16 and tau(17) + tau(18) + tau(19) + tau(20) = 2 + 6 + 2 + 6 = 16.

%e 21 is a term as tau(16) + ... + tau(20) = 5 + 2 + 6 + 2 + 6 = 21 and tau(22) + ... tau(26) = 4 + 2 + 8 + 3 + 4 = 21.

%Y Cf. A000005, A000203, A006218.

%K nonn

%O 1,1

%A _Scott R. Shannon_, Jul 04 2021