A350936 a(n) is the smallest number m such that tau(m) = n*tau(m-1) = n*tau(m+1) or 0 if no such m exists, where tau(k) = A000005(k).

34, 6, 12, 30, 816, 60, 192, 270, 180, 240, 56320, 420, 233472, 2112, 1620, 1320, 2162688, 2340, 786432, 3120, 4800, 15360, 62914560, 3360, 172368, 724992, 6300, 29760, 24964497408, 12240, 35433480192, 7560, 599040, 15138816, 81648, 21600, 7215545057280

Offset

1,1

Comments

Corresponding values of tau(a(n)): 4, 4, 6, 8, 20, 12, 14, 16, 18, 20, 44, 24, 52, 28, 30, 32, 68, 36, 38, 40, 42, 44, 92, 48, 100, 52, 54, 56, 116, 60, 124, 64, 132, 136, 70, 72, 296, ...

Triples of [tau(a(n) - 1), tau(a(n)), tau(a(n) + 1)] = [tau(a(n)) / n, tau(a(n)), tau(a(n)) / n]: [4, 4, 4], [2, 4, 2], [2, 6, 2], [2, 8, 2], [4, 20, 4], [2, 12, 2], [2, 14, 2], [2, 16, 2], [2, 18, 2], [2, 20, 2], [4, 44, 4], ...

Links

Table of n, a(n) for n=1..37.

Example

a(3) = 12 because 12 is the smallest number m such that tau(m) = 3 * tau(m-1) = 3 * tau(m+1); tau(12) = 3 * tau(11) = 3 * tau(13) = 3 * 2 = 6.

Prog

(Magma) Ax:=func<n|exists(r){m: m in[2..10^6] | n * #Divisors(m - 1) eq n * #Divisors(m + 1) and n * #Divisors(m + 1) eq #Divisors(m)} select r else 0>; [Ax(n): n in [1..16]]

Crossrefs

Cf. A000005, A190646, A350132, A350934, A350935.

Sequence in context: A328913 A269482 A037933 * A297875 A298138 A350935

Adjacent sequences: A350933 A350934 A350935 * A350937 A350938 A350939

Keyword

nonn

Author

Jaroslav Krizek, Jan 25 2022

Extensions

a(23)-a(37) from Jon E. Schoenfield, Jan 25 2022

Status

approved