A169834 Numbers k such that d(k-1) = d(k) = d(k+1).

34, 86, 94, 142, 202, 214, 218, 231, 243, 244, 302, 375, 394, 446, 604, 634, 664, 698, 903, 922, 1042, 1106, 1138, 1262, 1275, 1310, 1335, 1346, 1402, 1642, 1762, 1833, 1838, 1886, 1894, 1925, 1942, 1982, 2014, 2055, 2102, 2134, 2182, 2218, 2265, 2306, 2344, 2362

Offset: 1

Author

N. J. A. Sloane, Jun 02 2010

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)
• Erich Friedman, What's Special About This Number? (See entry 34.)

Crossrefs

Cf. A000005, A005238.

Cf. A051950.

Programs

Haskell

a169834 n = a169834_list !! (n-1)
a169834_list = f a051950_list [0..] where
   f (0:0:ws) (x:y:zs) = y : f (0:ws) (y:zs)
   f (:v:ws) (:y:zs) = f (v:ws) (y:zs)
-- Reinhard Zumkeller, Aug 31 2014

Maple

q:= n-> is(nops(map(numtheory[tau], {$n-1..n+1}))=1):
select(q, [$1..3000])[];  # Alois P. Heinz, Jun 24 2021

Mathematica

d[n_] := DivisorSigma[0, n];
samedQ[n_] := d[n-1] == d[n] == d[n+1];
Select[Range[3000], samedQ] (* Jean-François Alcover, Aug 01 2018 *)
1 + Flatten@Position[Differences@#&/@Partition[DivisorSigma[0, Range@3000], 3, 1], {0, 0}] (* Hans Rudolf Widmer, Feb 02 2023 *)

Python

from sympy import divisor_count as d
def ok(n): return d(n-1) == d(n) == d(n+1)
print(list(filter(ok, range(1, 2400)))) # Michael S. Branicky, Jun 24 2021

Formula

a(n) = A005238(n) + 1. - Jon Maiga / Georg Fischer, Jun 24 2021