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

1,1

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

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 *)

Prog

(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

Crossrefs

Cf. A000005.

Sequence in context: A063834 A139117 A226736 * A034464 A116696 A000220

Adjacent sequences: A066705 A066706 A066707 * A066709 A066710 A066711

Keyword

nonn

Author

Vladeta Jovovic, Jan 14 2002

Status

approved