A080756 Numbers k such that there are infinitely many multiples of k that have exactly k divisors.

8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 50, 52, 54, 56, 60, 63, 64, 68, 72, 75, 76, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 104, 108, 112, 116, 117, 120, 121, 124, 125, 126, 128, 132, 135, 136, 140, 144, 147, 148, 150, 152, 153, 156, 160

Offset

1,1

Comments

Regional Math Competition for Northwestern Bulgaria, Vraca 2003, Problem 12/3.

Sequence consists of all nonsquarefree numbers except for the number 4.

Links

Table of n, a(n) for n=1..61.

Example

8 is a term because all numbers of the form 2^3*p (where p is an odd prime) have exactly 8 divisors and are multiples of 8.
Any squarefree number has only a finite number of such multiples. The number 4 has only one such multiple (8).

Crossrefs

Cf. A013929.

Sequence in context: A347392 A179443 A264828 * A304661 A189833 A336711

Adjacent sequences: A080753 A080754 A080755 * A080757 A080758 A080759

Keyword

nonn

Author

Ivaylo Kortezov, Mar 09 2003

Extensions

Edited by Jon E. Schoenfield, Oct 28 2023

Status

approved