OFFSET
1,1
COMMENTS
Corresponding values of tau(a(n)): 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, ...
Triplets of [tau(a(n)), tau(a(n) + 1), tau(a(n) + 2)] = [tau(a(n)), tau(a(n)) + 1, tau(a(n))]: [2, 3, 2], [8, 9, 8], [8, 9, 8], [8, 9, 8], [8, 9, 8], [8, 9, 8], [8, 9, 8], [8, 9, 8], [8, 9, 8], ...
a(n) is one less than a perfect square. - David A. Corneth, Dec 29 2020
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000
EXAMPLE
tau(3) = 2, tau(4) = 3, tau(5) = 2.
MATHEMATICA
d1 = 1; d2 = 2; s = {}; Do[d3 = DivisorSigma[0, n]; If[Equal @@ {d1, d2 - 1, d3}, AppendTo[s, n - 2]]; d1 = d2; d2 = d3, {n, 3, 10^7}]; s (* Amiram Eldar, Dec 17 2020 *)
PROG
(Magma) [m: m in [2..10^6] | #Divisors(m + 1) - 1 eq #Divisors(m) and #Divisors(m + 2) eq #Divisors(m)]
(PARI) isok(m) = my(nb = numdiv(m)); (numdiv(m+2) == nb) && (numdiv(m+1) == nb+1); \\ Michel Marcus, Dec 18 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Dec 16 2020
EXTENSIONS
More terms from Amiram Eldar, Dec 16 2020
STATUS
approved