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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
OFFSET
1,2
COMMENTS
Intersection of A033950 and A262981.
LINKS
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
KEYWORD
nonn
AUTHOR
Vladimir Letsko, Dec 11 2016
STATUS
approved