A086552 Numbers x such that tau(x)/tau(x-1) is an integer, where tau() is the number of divisors function.

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

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