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).

34, 7, 19, 41, 6641, 199, 640063, 919, 17299, 22193, 350632961, 5741, 57394565119, 2345921, 3568049, 18089, 55171346530303, 41651, 193405731995647, 252881, 88099649, 1439024129, 916791443027132417, 90271, 821128751, 20969598977, 3959299, 2319679, 190190725057515297439745, 7860401

Offset

1,1

Comments

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, ...

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], ...

Links

Table of n, a(n) for n=1..30.

Example

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.

Prog

(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]]

Crossrefs

Cf. A000005, A190646, A350132, A350934, A350936.

Sequence in context: A350936 A297875 A298138 * A350132 A350934 A071788

Adjacent sequences: A350932 A350933 A350934 * A350936 A350937 A350938

Keyword

nonn

Author

Jaroslav Krizek, Jan 25 2022

Extensions

a(11)-a(16) from Jon E. Schoenfield, Jan 26 2022

More terms from Jon E. Schoenfield and David A. Corneth, Jan 27 2022

Status

approved