A279373 Numbers n such that number of divisors of n divides n and at the same time the least number having exactly n divisors is divisible by n.
1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 180, 225, 240, 252, 288, 360, 396, 441, 448, 450, 504, 560, 600, 625, 672, 720, 792, 880, 882, 936, 1040, 1056, 1200, 1248, 1250, 1260, 1344, 1408, 1440, 1620, 1664, 1680, 1800, 1980, 2000, 2016, 2025, 2160, 2176, 2240, 2340, 2640, 2700, 2772, 3120, 3168
Offset: 1
Keywords
Examples
8 is in the sequence because 8 is divisible by tau(8) and at the same time 8 divides 24 which is the least number having exactly 8 divisors.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..267
- A. Bundy, Simon Colton, T. Walsh, HR - A system for Machine Discovery in Finite Algebras, ECAI 1998.
- S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.
- S. Colton, HR - Automatic Theory Formation in Pure Mathematics
- Robert E. Kennedy and Curtis N. Cooper, Tau numbers, natural density and Hardy and Wright's Theorem 437, International Journal of Mathematics and Mathematical Sciences, 13:2 (1990), pp. 383-386.
- Claudia Spiro, How often is the number of divisors of n a divisor of n?, J. Number Theory 21 (1985), no. 1, 81-100.
- Vladimir Letsko, Mathematical Marathon, Problem 216 (in Russian)
Programs
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Mathematica
Function[s, Select[TakeWhile[#, KeyExistsQ[s, #] &], Divisible[Lookup[s, #], #] &] &@ Select[Range@ 3000, Divisible[#, DivisorSigma[0, #]] &]]@ Map[First, KeySort@ PositionIndex@ Table[DivisorSigma[0, n], {n, 10^7}]] (* Michael De Vlieger, Dec 11 2016, Version 10 *)
Comments