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

Author

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

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000384.

Programs

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 *)

Extensions

More terms from Emeric Deutsch, Apr 06 2006