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

1,2

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Intersection of A028839 and A174800.

Sequence in context: A061766 A109448 A177927 * A030754 A244863 A077584

Adjacent sequences: A062395 A062396 A062397 * A062399 A062400 A062401

Keyword

nonn,base,easy

Author

Amarnath Murthy, Jun 28 2001

Extensions

Corrected and extended by Erich Friedman, Jul 02 2001

Status

approved