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A117064 Hexagonal numbers for which both the sum of the digits and the product of the digits are also hexagonal numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 28 16:56 EDT 2022. Contains 354907 sequences. (Running on oeis4.)