A116565 Hexagonal numbers whose number of divisors is also a hexagonal number.

1, 28, 45, 153, 325, 4753, 7381, 29161, 56953, 65341, 73536, 166753, 266085, 270480, 354061, 1062153, 1383616, 3123750, 3525840, 3873936, 5247180, 5649841, 6060421, 6644835, 6835753, 6924781, 7006896, 7870528, 9925740, 10285380, 12708361

Offset

1,2

Comments

The hexagonal numbers are numbers of the form n(2n-1) (A000384).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..500

Example

45 is in the sequence because 45=5(2*5-1) is a hexagonal number having 6 divisors (1,3,5,9,15,45) and 6=2(2*2-1) is also a hexagonal number.

Maple

with(numtheory): a:=proc(n) local h: h:=tau(n*(2*n-1)): if type(sqrt(1+8*h)/4+1/4, integer) then n*(2*n-1) else fi end: seq(a(n), n=0..3000); # Emeric Deutsch, Apr 06 2006

Mathematica

With[{hex=PolygonalNumber[6, Range[3000]]}, Select[hex, MemberQ[hex, DivisorSigma[0, #]]&]] (* Harvey P. Dale, Mar 10 2024 *)

Crossrefs

Cf. A000384.

Sequence in context: A332764 A116541 A292989 * A305060 A039615 A046419

Adjacent sequences: A116562 A116563 A116564 * A116566 A116567 A116568

Keyword

nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 03 2006

Extensions

More terms from Emeric Deutsch, Apr 06 2006

Status

approved