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

1,2

Comments

Intersection of A033950 and A262981.

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)

Example

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.

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 *)

Crossrefs

Cf. A000005, A005179, A033950, A262981, A262983.

Sequence in context: A162952 A033950 A046526 * A057529 A336715 A120737

Adjacent sequences: A279370 A279371 A279372 * A279374 A279375 A279376

Keyword

nonn

Author

Vladimir Letsko, Dec 11 2016

Status

approved