login
Least m such that n = m mod tau(m) if such m exists, otherwise 0.
2

%I #10 Mar 15 2023 10:54:49

%S 3,6,15,28,165,30,135,48,144,192,1755,300,1485,270,2079,336,6237,1008,

%T 9639,1728,1296,3510,28215,1080,16900,2970,10395,7840,12285,4158,

%U 41055,4752,40425,12474,48195,3780,220077,19278,51975,10920,356265,9450

%N Least m such that n = m mod tau(m) if such m exists, otherwise 0.

%C By definition, a(n) >= n. If the condition is changed to n == m mod tau(m), then a(n) = 1 for all n. - _Chai Wah Wu_, Mar 14 2023

%H Chai Wah Wu, <a href="/A066708/b066708.txt">Table of n, a(n) for n = 1..270</a>

%t Module[{nn=500000,mtm},mtm=Table[{m,Mod[m,DivisorSigma[0,m]]},{m,nn}];Table[ SelectFirst[mtm,#[[2]]==n&],{n,50}]][[All,1]] (* _Harvey P. Dale_, Jan 10 2023 *)

%o (Python)

%o from itertools import count

%o from sympy import divisor_count

%o def A066708(n): return next(filter(lambda m:m%divisor_count(m)==n,count(n))) # _Chai Wah Wu_, Mar 14 2023

%Y Cf. A000005.

%K nonn

%O 1,1

%A _Vladeta Jovovic_, Jan 14 2002