A062398 Numbers such that the product of the digits and the sum of the digits are squares.

1, 4, 9, 10, 22, 40, 88, 90, 100, 103, 108, 130, 144, 180, 202, 207, 220, 270, 301, 306, 310, 360, 400, 405, 414, 441, 450, 466, 504, 540, 603, 630, 646, 664, 702, 709, 720, 790, 801, 808, 810, 880, 889, 898, 900, 907, 970, 988, 1000, 1003, 1008, 1012, 1017

Offset: 1

Author

Amarnath Murthy, Jun 28 2001

Keywords

• nonn
• base
• easy

Examples

			144 belongs to the sequence as sum of digits = 9 and the product of the digits = 16.
		

Links

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

Crossrefs

Intersection of A028839 and A174800.

Programs

Mathematica

pdsdQ[n_]:=Module[{idn=IntegerDigits[n]},IntegerQ[Sqrt[Total[idn]]] && IntegerQ[Sqrt[Times@@idn]]]; Select[Range[1100],pdsdQ] (* Harvey P. Dale, Aug 20 2012 *)

PARI

isok(k)={my(d=digits(k)); issquare(vecsum(d)) && issquare(vecprod(d))} \\ Harry J. Smith, Aug 07 2009

Extensions

Corrected and extended by Erich Friedman, Jul 02 2001