The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A086552 Numbers x such that tau(x)/tau(x-1) is an integer, where tau() is the number of divisors function. 1
 2, 3, 6, 8, 12, 14, 15, 18, 20, 22, 24, 27, 30, 32, 34, 35, 38, 39, 40, 42, 44, 45, 48, 50, 54, 56, 58, 60, 62, 66, 68, 70, 72, 74, 76, 78, 80, 84, 86, 87, 88, 90, 94, 95, 96, 98, 99, 102, 104, 105, 108, 110, 114, 117, 119, 120, 123, 126, 128, 130, 132, 134, 135, 136, 138 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: (1) tau(x)/tau(x-1) = n has solutions for every n. (2) If x is the smallest number for a given n such that tau(x)/tau(x-1) = n > 1, then x-1 is a prime. LINKS Jinyuan Wang, Table of n, a(n) for n = 1..10000 EXAMPLE 12 is a member as tau(12)/tau(11) = 3, 15 is a member as tau(15)/tau(14) = 1. MAPLE with(numtheory): a:=proc(n) if type(tau(n)/tau(n-1), integer)=true then n else fi end: seq(a(n), n=2..150); # Emeric Deutsch, Mar 25 2005 PROG (PARI) isok(n) = denominator(numdiv(n)/numdiv(n-1)) == 1; \\ Michel Marcus, Apr 12 2018 CROSSREFS Cf. A057922, A086550, A086551. Sequence in context: A025053 A140496 A308843 * A098393 A263883 A103567 Adjacent sequences:  A086549 A086550 A086551 * A086553 A086554 A086555 KEYWORD nonn AUTHOR Amarnath Murthy, Aug 28 2003 EXTENSIONS More terms from David Wasserman and Emeric Deutsch, Mar 25 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 3 05:38 EDT 2020. Contains 336197 sequences. (Running on oeis4.)