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%I #16 Mar 28 2023 21:13:19
%S 1,4,9,10,22,40,88,90,100,103,108,130,144,180,202,207,220,270,301,306,
%T 310,360,400,405,414,441,450,466,504,540,603,630,646,664,702,709,720,
%U 790,801,808,810,880,889,898,900,907,970,988,1000,1003,1008,1012,1017
%N Numbers such that the product of the digits and the sum of the digits are squares.
%H Harry J. Smith, <a href="/A062398/b062398.txt">Table of n, a(n) for n = 1..1000</a>
%e 144 belongs to the sequence as sum of digits = 9 and the product of the digits = 16.
%t pdsdQ[n_]:=Module[{idn=IntegerDigits[n]},IntegerQ[Sqrt[Total[idn]]] && IntegerQ[Sqrt[Times@@idn]]]; Select[Range[1100],pdsdQ] (* _Harvey P. Dale_, Aug 20 2012 *)
%o (PARI) SumD(x)= { s=0; while (x>9, s+=x-10*(x\10); x\=10); return(s + x) } ProdD(x)= { p=1; while (x>9, p*=(x-10*(x\10)); x\=10); return(p*x) } { n=0; for (m=1, 10^9, if (issquare(ProdD(m)) && issquare(SumD(m)), write("b062398.txt", n++, " ", m); if (n==1000, break)) ) } \\ _Harry J. Smith_, Aug 07 2009
%Y Cf. A028839.
%K nonn,base,easy
%O 1,2
%A _Amarnath Murthy_, Jun 28 2001
%E Corrected and extended by _Erich Friedman_, Jul 02 2001
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