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Another variant of narcissistic numbers: integers n equal the product of squared digits of n divided by the sum of digits of n, i.e., n = A007954(n)^2/A007953(n).
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%I #23 May 31 2018 14:51:13

%S 1,2,3,4,5,6,7,8,9,36,735

%N Another variant of narcissistic numbers: integers n equal the product of squared digits of n divided by the sum of digits of n, i.e., n = A007954(n)^2/A007953(n).

%C No other terms below 10^300. - _Max Alekseyev_, May 31 2018

%e 36 is a term because 36 = (3^2*6^2)/(3+6).

%e 735 is a term because 735 = (7^2*3^2*5^2)/(7+3+5).

%t Select[Range[10^6], Function[k, k == Apply[Times, #^2]/(Total@ #) &@ IntegerDigits@ k]@ # &] (* _Michael De Vlieger_, Mar 16 2016 *)

%o (PARI) { is_A270393(n) = my(d = digits(n)); n == vecprod(d)^2/vecsum(d); } \\ _Michel Marcus_, Mar 17 2016

%Y Subsequence of A128606.

%Y Cf. A005188, A257554.

%K nonn,more,base

%O 1,2

%A _José de Jesús Camacho Medina_, Mar 16 2016