A116565 - OEIS

%I #12 Mar 10 2024 16:36:31

%S 1,28,45,153,325,4753,7381,29161,56953,65341,73536,166753,266085,

%T 270480,354061,1062153,1383616,3123750,3525840,3873936,5247180,

%U 5649841,6060421,6644835,6835753,6924781,7006896,7870528,9925740,10285380,12708361

%N Hexagonal numbers whose number of divisors is also a hexagonal number.

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

%H Harvey P. Dale, <a href="/A116565/b116565.txt">Table of n, a(n) for n = 1..500</a>

%e 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.

%p 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

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

%Y Cf. A000384.

%K nonn

%O 1,2

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

%E More terms from _Emeric Deutsch_, Apr 06 2006