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 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. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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. 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

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Last modified May 26 13:59 EDT 2022. Contains 354092 sequences. (Running on oeis4.)