A339776 Numbers m such that tau(m) = tau(m + 1) - 1 = tau(m + 2), where tau(k) = the number of divisors of k (A000005).

3, 252003, 293763, 770883, 1444803, 2630883, 6543363, 8421603, 9375843, 18992163, 19731363, 21883683, 22108803, 25786083, 25989603, 32512803, 35259843, 48972003, 98049603, 101566083, 132204003, 155201763, 160224963, 162766563, 187197123, 208455843, 291658083

Offset: 1

Author

Jaroslav Krizek, Dec 16 2020

Keywords

• nonn

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

Examples

			tau(3) = 2, tau(4) = 3, tau(5) = 2.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A339777.

Subsequence of A005563.

Intersection of A062832 and A055927.

Programs

Magma

[m: m in [2..10^6] | #Divisors(m + 1) - 1 eq #Divisors(m) and #Divisors(m + 2) eq #Divisors(m)]

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 *)

PARI

isok(m) =  my(nb = numdiv(m)); (numdiv(m+2) == nb) && (numdiv(m+1) == nb+1); \\ Michel Marcus, Dec 18 2020

Extensions

More terms from Amiram Eldar, Dec 16 2020