A117064 Hexagonal numbers for which both the sum of the digits and the product of the digits are also hexagonal numbers.

0, 1, 6, 231, 780, 1770, 2850, 3003, 4560, 14028, 17205, 20301, 20706, 24090, 24531, 28203, 32640, 37401, 43071, 80601, 96580, 102831, 103740, 112101, 191890, 200661, 201930, 239086, 255970, 286903, 296065, 302253, 303810, 316410, 318003, 332520

Offset

1,3

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

24531 is in the sequence because it is a hexagonal number, the sum of its digits 2+4+5+3+1=15 is a hexagonal number and the product of its digits 2*4*5*3*1=120 is also a hexagonal number.

Mathematica

hexQ[n_] := n == 0 || IntegerQ[(Sqrt[8 n + 1] + 1)/4]; t = {0}; Do[h = n*(2 n - 1); If[hexQ[Plus @@ (z = IntegerDigits[h])] && hexQ[Times @@ z], AppendTo[t, h]], {n, 410}]; t (* Jayanta Basu, Jul 13 2013 *)

Prog

(PARI) is(n) = isHexagonal(n) && isHexagonal(sumdigits(n)) && isHexagonal(vecprod(digits(n)))
isHexagonal(n) = { my(c = (sqrtint(8*n + 1) + 1)>>2); c*(2*c - 1) == n } \\ David A. Corneth, Feb 06 2021

Crossrefs

Cf. A000384, A007953, A007954.

Sequence in context: A277293 A177043 A309009 * A112001 A286314 A099124

Adjacent sequences: A117061 A117062 A117063 * A117065 A117066 A117067

Keyword

nonn,base

Author

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

Extensions

Offset corrected by David A. Corneth, Feb 06 2021

Status

approved