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A117063
Hexagonal numbers for which the product of the digits is also a hexagonal number.
1
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
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
Sequence in context: A290341 A246827 A127726 * A178911 A227027 A001219
KEYWORD
base,nonn
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), Apr 16 2006
EXTENSIONS
Offset corrected by Amiram Eldar, Feb 06 2021
STATUS
approved