A066708 Least m such that n = m mod tau(m) if such m exists, otherwise 0.

3, 6, 15, 28, 165, 30, 135, 48, 144, 192, 1755, 300, 1485, 270, 2079, 336, 6237, 1008, 9639, 1728, 1296, 3510, 28215, 1080, 16900, 2970, 10395, 7840, 12285, 4158, 41055, 4752, 40425, 12474, 48195, 3780, 220077, 19278, 51975, 10920, 356265, 9450

Offset: 1

Author

Vladeta Jovovic, Jan 14 2002

Keywords

• nonn

Comments

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..270

Crossrefs

Cf. A000005.

Programs

Mathematica

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 *)

Python

from itertools import count
from sympy import divisor_count
def A066708(n): return next(filter(lambda m:m%divisor_count(m)==n,count(n))) # Chai Wah Wu, Mar 14 2023