A117063 Hexagonal numbers for which the product of the digits is also a hexagonal number.

0, 1, 6, 120, 153, 190, 231, 630, 703, 780, 1035, 1540, 1770, 2016, 2701, 2850, 3003, 3160, 4005, 4560, 4950, 6670, 6903, 7140, 9180, 9730, 10011, 10296, 10585, 10878, 12090, 12403, 12720, 13041, 14028, 14706, 15051, 15400, 16110, 17205, 19110

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

24531 is in the sequence because (1) it is a hexagonal number and (2) the product of its digits 2*4*5*3*1 = 120 is also a hexagonal number.

Mathematica

pod[n_] := Times @@ IntegerDigits[n]; hexQ[n_] := n == 0 || IntegerQ[(Sqrt[32*n + 4] + 2)/8]; Select[Table[n*(2*n - 1), {n, 0, 120}], hexQ[pod[#]] &] (* Amiram Eldar, Feb 06 2021 *)
Module[{nn=100, hx}, hx=PolygonalNumber[6, Range[0, nn]]; Select[hx, MemberQ[ hx, Times@@ IntegerDigits[ #]]&]] (* Harvey P. Dale, Aug 24 2022 *)

Crossrefs

Cf. A000384, A007954.

Sequence in context: A290341 A246827 A127726 * A178911 A227027 A001219

Adjacent sequences: A117060 A117061 A117062 * A117064 A117065 A117066

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 16 2006

Extensions

Offset corrected by Amiram Eldar, Feb 06 2021

Status

approved