A244857 Numbers divisible by both the sum of the squares of their digits and the product of their digits.

1, 111, 315, 1344, 3312, 4416, 6624, 11112, 12312, 31311, 114192, 121716, 134112, 134136, 141312, 231336, 282624, 313416, 314112, 411648, 431136, 613116, 628224, 1112232, 1112832, 1121232, 1122112, 1122312, 1122912, 1143216, 1211232, 1212112, 1212192, 1212312

Offset: 1

Author

Michel Lagneau, Jul 07 2014

Keywords

• nonn
• base

Comments

Subsequence of A034087.

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].

Intersection of A034087 and A007602. - Jens Kruse Andersen, Jul 13 2014

Examples

			315 is in the sequence because 3^2+1^2+5^2 = 35 divides 315 and 3*1*5 = 15 divides 315.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007602, A034087, A038186, A117562.

Programs

Mathematica

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]

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