

A086552


Numbers x such that tau(x)/tau(x1) 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
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OFFSET

1,1


COMMENTS

Conjecture: (1) tau(x)/tau(x1) = n has solutions for every n. (2) If x is the smallest number for a given n such that tau(x)/tau(x1) = n > 1, then x1 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(n1), 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(n1)) == 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



