cp's OEIS Frontend

A350935 a(n) is the smallest number m such that tau(m-1) = tau(m+1) = n*tau(m) or 0 if no such m exists, where tau(k) = A000005(k).

%I A350935 #22 Feb 20 2022 22:45:13
%S A350935 34,7,19,41,6641,199,640063,919,17299,22193,350632961,5741,
%T A350935 57394565119,2345921,3568049,18089,55171346530303,41651,
%U A350935 193405731995647,252881,88099649,1439024129,916791443027132417,90271,821128751,20969598977,3959299,2319679,190190725057515297439745,7860401
%N A350935 a(n) is the smallest number m such that tau(m-1) = tau(m+1) = n*tau(m) or 0 if no such m exists, where tau(k) = A000005(k).
%C A350935 Corresponding values of tau(a(n)): 4, 2, 2, 2, 4, 2, 4, 2, 2, 2, 4, 2, 8, 2, 4, 2, 8, 2, 4, 2, 4, 4, 8, 2, 4, 4, 2, 2, 8, 2, ...
%C A350935 Triples of [tau(a(n) - 1), tau(a(n)), tau(a(n) + 1)] = [n * tau(a(n)), tau(a(n)), n * tau(a(n))]: [4, 4, 4], [4, 2, 4], [6, 2, 6], [8, 2, 8], [20, 4, 20], [12, 2, 12], [28, 4, 28], [16, 2, 16], [18, 2, 18], [20, 2, 20], ...
%e A350935 a(3) = 19 because 19 is the smallest number m such that tau(m-1) = tau(m+1) = 3 * tau(m); tau(18) = tau(20) = 3 * tau(19) = 3 * 2 = 6.
%o A350935 (Magma) Ax:=func<n|exists(r){m: m in[2..10^6] | #Divisors(m - 1) eq n * #Divisors(m) and #Divisors(m + 1) eq n * #Divisors(m)} select r else 0>; [Ax(n): n in [1..10]]
%Y A350935 Cf. A000005, A190646, A350132, A350934, A350936.
%K A350935 nonn
%O A350935 1,1
%A A350935 _Jaroslav Krizek_, Jan 25 2022
%E A350935 a(11)-a(16) from _Jon E. Schoenfield_, Jan 26 2022
%E A350935 More terms from _Jon E. Schoenfield_ and _David A. Corneth_, Jan 27 2022