A206368 Numbers k such that A206369(k) = A206369(k + 1).

1, 20, 116, 135, 171, 194, 740, 1220, 1419, 1803, 1892, 1952, 2696, 3705, 4575, 5186, 7868, 10659, 11247, 17948, 18507, 18548, 19107, 25545, 27405, 29294, 33500, 34371, 37820, 48872, 49184, 53108, 54620, 58652, 61760, 67220, 102296, 104139, 105908, 113576

Offset: 1

Author

N. J. A. Sloane, Feb 06 2012

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000 (terms 1..100 from Reinhard Zumkeller)
• László Tóth, A survey of the alternating sum-of-divisors function, arXiv:1111.4842 [math.NT], 2011-2014.

Crossrefs

Cf. A206369, A206475.

Programs

Haskell

import Data.List (elemIndices)
a206368 n = a206368_list !! (n-1)
a206368_list = map (+ 1) $ elemIndices 0 a206475_list
-- Reinhard Zumkeller, Feb 08 2012

Mathematica

(* b = A206369 *) b[n_] := n*DivisorSum[n, LiouvilleLambda[#]/# &];
Reap[For[n = 1, n <= 120000, n++, If[b[n] == b[n+1], Print[n]; Sow[n] ] ] ][[2, 1]] (* Jean-François Alcover, Dec 04 2017 *)

Python

from math import prod; from sympy import factorint
def A206369(n): return prod((lambda x:x[0]+int((x[1]<<1)>=p+1))(divmod(p**(e+1), p+1)) for p, e in factorint(n).items())
for n in range(1,10001):
    if A206369(n) == A206369(n+1):
        print(n,end=', ')
# Shreyansh Jaiswal, May 02 2025

Formula

A206475(a(n)) = 0. - Reinhard Zumkeller, Feb 08 2012