A257172 Consider numbers n = concat(w,x,y,z) such that w*x*y*z | n. Leading zeros in x, y and z allowed. Sequence lists numbers that admit at least two such concatenations.

11424, 13248, 14112, 16128, 16632, 17136, 18144, 41328, 91728, 101112, 102144, 102816, 104832, 106272, 111012, 111375, 112288, 112896, 114048, 114240, 114912, 116160, 116928, 123120, 132480, 140112, 141120, 161280, 166320, 171171, 171360, 181440, 203112, 204288, 204336, 220416, 231012, 233772, 239616

Offset

1,1

Links

Table of n, a(n) for n=1..39.

Example

11424 / (1*1*4*24)=119, 11424 / (1*1*42*4)=68 and 11424 / (1 14*2*4)  but 11424 / (11*4*2*4) is 357/11, not an integer. So 11424 is the concatenation of three sets of four integers whose products divide 11424.

Maple

with(numtheory); P:=proc(q) local a, ab, b, c, cd, d, i, j, k, m, n, v, w, z;
v:=array(1..10, 1..4); w:=[]; for n from 1 to q do j:=0;
for i from 1 to ilog10(n) do c:=(n mod 10^i); ab:=trunc(n/10^i);
for k from 1 to ilog10(ab) do d:=(ab mod 10^k); cd:=trunc(ab/10^k);
for z from 1 to ilog10(cd) do a:=trunc(cd/10^z); b:=cd-a*10^z;
if a*b*c*d>0 then if type(n/(a*b*c*d), integer) then j:=j+1;
w:=sort([a, b, c, d]); for m from 1 to 4 do v[j, m]:=w[m]; od;
for m from 1 to j-1 do if v[m, 1]=v[j, 1] and v[m, 2]=v[j, 2] and v[m, 3]=v[j, 3] and v[m, 4]=v[j, 4]
then j:=j-1; break; fi; od; fi; fi; od; od; od;
if j>1 then print(n); fi; od; end: P(10^9);

Mathematica

fQ[n_] := Block[{id = IntegerDigits@ n}, lng = Length@ id; t = Times @@@ Union[ Sort /@ Partition[ Flatten@ Table[{FromDigits@ Take[id, {1, i}], FromDigits@ Take[id, {i + 1, j}], FromDigits@ Take[id, {j + 1, k}], FromDigits@ Take[id, {k + 1, lng}]}, {i, 1, lng - 3}, {j, i + 1, lng - 2}, {k, j + 1, lng - 1}], 4]]; Count[IntegerQ /@ (n/t), True] > 1]; k = 1000; lst = {}; While[k < 100000001, If[fQ@ k, AppendTo[lst, k]]; k++]; lst

Crossrefs

Cf. A256518.

Sequence in context: A157655 A262399 A115753 * A269217 A154064 A140922

Adjacent sequences: A257169 A257170 A257171 * A257173 A257174 A257175

Keyword

nonn,base

Author

Paolo P. Lava and Robert G. Wilson v, Apr 17 2015

Status

approved