A190644 Least number k>1 such that (tau(k-1)+tau(k+1))/tau(k) = n where tau = A000005.

6, 34, 39, 7, 11, 19, 29, 41, 79, 71, 179, 199, 181, 239, 883, 419, 701, 839, 881, 1429, 2351, 1259, 1871, 2161, 4049, 3079, 3361, 2521, 6481, 4159, 6299, 5279, 11551, 5039, 20789, 7561, 25919, 10079, 16561, 13441, 38611, 13859, 23761, 21839, 100673, 20161

Offset: 1

Author

Juri-Stepan Gerasimov, May 15 2011

Keywords

• nonn

Crossrefs

Cf. A000005 (number of divisors of n), A190612.

Programs

Maple

with(numtheory):
a:= proc(n) local k;
      for k from 2 while (tau(k-1)+tau(k+1)) /tau(k)<>n do od; k
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, May 19 2011

Mathematica

tau = DivisorSigma[0, #]&;
a[n_] := For[k=2, True, k++, If[(tau[k-1]+tau[k+1])/tau[k]==n, Return[k]]];
Array[a, 50] (* Jean-François Alcover, Mar 27 2017 *)
Module[{nn=300000,tau},tau=(#[[1]]+#[[3]])/#[[2]]&/@Partition[DivisorSigma[ 0,Range[nn]],3,1];Flatten[Table[Position[tau,n,1,1],{n,50}]]+1] (* Harvey P. Dale, Nov 24 2022 *)

Sage

def A190644(n):
    tau = number_of_divisors
    return next((k for k in IntegerRange(2,infinity) if tau(k-1)+tau(k+1) == n*tau(k))) # D. S. McNeil, May 19 2011