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%I #16 Mar 30 2021 12:02:47
%S 1,111,315,1344,3312,4416,6624,11112,12312,31311,114192,121716,134112,
%T 134136,141312,231336,282624,313416,314112,411648,431136,613116,
%U 628224,1112232,1112832,1121232,1122112,1122312,1122912,1143216,1211232,1212112,1212192,1212312
%N Numbers divisible by both the sum of the squares of their digits and the product of their digits.
%C Subsequence of A034087.
%C The property "numbers divisible by the sum of the squares and product of their digits" leads to the Diophantine equation t*x1*x2*...*xr=s*(x1^2+x2^2+...+xr^2), where t and s are divisors of n; xi is from [1...9].
%C Intersection of A034087 and A007602. - _Jens Kruse Andersen_, Jul 13 2014
%H David A. Corneth, <a href="/A244857/b244857.txt">Table of n, a(n) for n = 1..10000</a>
%e 315 is in the sequence because 3^2+1^2+5^2 = 35 divides 315 and 3*1*5 = 15 divides 315.
%t dspQ[n_]:=Module[{idn=IntegerDigits[n], t}, t=Times@@idn; t!=0 && Divisible[n, Total[idn^2]] && Divisible[n, t]]; Select[Range[2*10^6], dspQ]
%o (PARI) isok(n) = (d = digits(n)) && (prd = prod(i=1, #d, d[i])) && !(n % prd) && !(n % sum(i=1, #d, d[i]^2)); \\ _Michel Marcus_, Jul 07 2014
%Y Cf. A007602, A034087, A038186, A117562.
%K nonn,base
%O 1,2
%A _Michel Lagneau_, Jul 07 2014
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