A339778 Numbers m such that numbers m, m + 1 and m + 2 have k, 2k and 3k divisors respectively.

61, 73, 277, 421, 458, 493, 583, 1234, 1393, 1418, 1658, 1909, 1954, 2066, 2138, 2234, 2329, 2386, 2533, 2594, 2773, 2797, 2846, 3013, 3073, 3265, 3394, 3841, 4322, 4333, 4538, 4586, 4633, 4717, 4754, 4766, 5029, 5223, 5245, 5342, 5378, 5554, 5893, 5906, 6169

Offset

1,1

Comments

Numbers m such that tau(m) = tau(m + 1) / 2 = tau(m + 2) / 3, where tau(k) = the number of divisors of k (A000005).

Corresponding values of tau(a(n)): 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4, ...

Triplets of [tau(a(n)), tau(a(n) + 1), tau(a(n) + 2)] = [tau(a(n)), 2*tau(a(n)), 3*tau(a(n))]: [2, 4, 6], [2, 4, 6], [2, 4, 6], [2, 4, 6], [4, 8, 12], [4, 8, 12], [4, 8, 12], [4, 8, 12], [4, 8, 12], ...

Links

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

Example

tau(61) = 2, tau(62) = 4, tau(63) = 6.

Mathematica

Select[Range[6000], Equal @@ (DivisorSigma[0, # + {0, 1, 2}]/{1, 2, 3}) &] (* Amiram Eldar, Dec 16 2020 *)

Prog

(Magma) [m: m in [1..10^5] | #Divisors(m) eq #Divisors(m + 1) / 2 and #Divisors(m) eq #Divisors(m + 2) / 3]
(PARI) isok(m) = my(nb = numdiv(m)); (numdiv(m+1) == 2*nb) && (numdiv(m+2) == 3*nb); \\ Michel Marcus, Dec 18 2020

Crossrefs

Cf. A000005, A100363.

Subsequence of A063446.

Sequence in context: A260808 A141457 A112998 * A328160 A118162 A217076

Adjacent sequences: A339775 A339776 A339777 * A339779 A339780 A339781

Keyword

nonn,changed

Author

Jaroslav Krizek, Dec 16 2020

Status

approved