A339776 -id:A339776 - cp's OEIS frontend

A339777 Numbers m such that tau(m) = tau(m + 1) + 1 = tau(m + 2), where tau(k) = the number of divisors of k (A000005).

8, 110888, 149768, 1119363, 1172888, 2676495, 3143528, 4782968, 5895183, 8596623, 9168783, 15896168, 19114383, 28174863, 48052623, 50523663, 58186383, 72641528, 82664463, 98168463, 113465103, 139523343, 178810383, 208860303, 223681935, 230675343, 248755983, 249260943

Offset: 1

Jaroslav Krizek, Dec 16 2020

nonn

Corresponding values of tau(a(n)): 4, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, ...
Triplets of [tau(a(n)), tau(a(n) + 1), tau(a(n) + 2)] = [tau(a(n)), tau(a(n)) - 1, tau(a(n))]: [4, 3, 4], [16, 15, 16], [16, 15, 16], [16, 15, 16], [16, 15, 16], [16, 15, 16], [16, 15, 16], [16, 15, 16], [16, 15, 16], ...
a(n) is one less than a perfect square. - David A. Corneth, Dec 29 2020

			tau(8) = 4, tau(9) = 3, tau(10) = 4.

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

Cf. A000005, A339776.
Subsequence of A005563.
Intersection of A062832 and A068208.

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

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 *)
Position[Partition[DivisorSigma[0,Range[59*10^5]],3,1],?(#[[1]]==#[[2]]+1==#[[3]]&),1,Heads->False]//Flatten (* _Harvey P. Dale, May 25 2023 *)

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

More terms from Amiram Eldar, Dec 16 2020

cp's OEIS Frontend

A339777 Numbers m such that tau(m) = tau(m + 1) + 1 = tau(m + 2), where tau(k) = the number of divisors of k (A000005).

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