A066567 Numbers that when incremented by the product of their digits produce a square.

2, 8, 13, 63, 91, 100, 128, 185, 215, 221, 337, 400, 448, 456, 549, 551, 559, 681, 900, 1024, 1089, 1151, 1185, 1215, 1221, 1327, 1348, 1437, 1600, 1651, 1897, 2025, 2112, 2191, 2196, 2209, 2293, 2304, 2392, 2401, 2448, 2500, 2539, 2544, 2551, 2596, 2601

Offset: 1

Author

Amarnath Murthy, Dec 18 2001

Keywords

• base
• nonn

Examples

			63 belongs to this sequence as 63 + 6*3 = 81 = 9^2.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000290, A066564, A230099.

Programs

Mathematica

f[n_] := n + Apply[ Times, IntegerDigits[n]]; Select[ Range[ 2500], IntegerQ[ Sqrt[ f[ # ]]] & ]
Select[Range[3000],IntegerQ[Sqrt[#+Times@@IntegerDigits[#]]]&] (* Harvey P. Dale, Sep 15 2024 *)

PARI

isok(k) = issquare(k+vecprod(digits(k))); \\ Harry J. Smith, Mar 05 2010

Extensions

More terms from Robert G. Wilson v, Dec 22 2001

Offset changed from 0 to 1 by Harry J. Smith, Mar 05 2010