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A244857 Numbers divisible by both the sum of the squares of their digits and the product of their digits. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

Table of n, a(n) for n=1..34.

EXAMPLE

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

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]

PROG

(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

CROSSREFS

Cf. A007602, A034087, A038186, A117562.

Sequence in context: A097650 A271312 A171773 * A225329 A277960 A304831

Adjacent sequences:  A244854 A244855 A244856 * A244858 A244859 A244860

KEYWORD

nonn,base,easy

AUTHOR

Michel Lagneau, Jul 07 2014

STATUS

approved

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Last modified October 20 02:18 EDT 2019. Contains 328244 sequences. (Running on oeis4.)