cp's OEIS Frontend

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

%I A206368 #35 May 02 2025 22:37:13
%S A206368 1,20,116,135,171,194,740,1220,1419,1803,1892,1952,2696,3705,4575,
%T A206368 5186,7868,10659,11247,17948,18507,18548,19107,25545,27405,29294,
%U A206368 33500,34371,37820,48872,49184,53108,54620,58652,61760,67220,102296,104139,105908,113576
%N A206368 Numbers k such that A206369(k) = A206369(k + 1).
%H A206368 Amiram Eldar, <a href="/A206368/b206368.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..100 from Reinhard Zumkeller)
%H A206368 László Tóth, <a href="http://arxiv.org/abs/1111.4842">A survey of the alternating sum-of-divisors function</a>, arXiv:1111.4842 [math.NT], 2011-2014.
%F A206368 A206475(a(n)) = 0. - _Reinhard Zumkeller_, Feb 08 2012
%t A206368 (* b = A206369 *) b[n_] := n*DivisorSum[n, LiouvilleLambda[#]/# &];
%t A206368 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 *)
%o A206368 (Haskell)
%o A206368 import Data.List (elemIndices)
%o A206368 a206368 n = a206368_list !! (n-1)
%o A206368 a206368_list = map (+ 1) $ elemIndices 0 a206475_list
%o A206368 -- _Reinhard Zumkeller_, Feb 08 2012
%o A206368 (Python)
%o A206368 from math import prod; from sympy import factorint
%o A206368 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())
%o A206368 for n in range(1,10001):
%o A206368     if A206369(n) == A206369(n+1):
%o A206368         print(n,end=', ')
%o A206368 # _Shreyansh Jaiswal_, May 02 2025
%Y A206368 Cf. A206369, A206475.
%K A206368 nonn
%O A206368 1,2
%A A206368 _N. J. A. Sloane_, Feb 06 2012