

A115569


LynchBell numbers: numbers n such that the digits are all different (and do not include 0) and n is divisible by each of its individual digits.


9



1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 24, 36, 48, 124, 126, 128, 132, 135, 162, 168, 175, 184, 216, 248, 264, 312, 315, 324, 384, 396, 412, 432, 612, 624, 648, 672, 728, 735, 784, 816, 824, 864, 936, 1236, 1248, 1296, 1326, 1362, 1368, 1395, 1632, 1692, 1764, 1824
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

This is a subset of some of the related sequences listed below. Stephen Lynch and Andrew Bell are Brisbane surgeons who contributed to the identification of this sequence.
There are 548 LynchBell numbers. A117911 gives the number of ndigit ones. The digit 5 cannot appear in LynchBell numbers containing an even digit; 5 must be the units digit when it appears. The 7digit LynchBell numbers are 105 permutations of 1289736 (the smallest such).  Rick L. Shepherd, Apr 01 2006
Can be seen/read as a table with row lengths A117911 (rows r > 7 have zero length).  M. F. Hasler, Jan 31 2016


LINKS

Rick L. Shepherd, List of all terms


EXAMPLE

384/3 = 128, 384/8 = 48, 384/4 = 96. Thus 384 is LynchBell as it is a multiple of each of its three distinct digits.


MATHEMATICA

Reap[For[n = 1, n < 10^7, n++, id = IntegerDigits[n]; If[FreeQ[id, 0] && Length[id] == Length[Union[id]] && And @@ (Divisible[n, #]& /@ id), Print[n]; Sow[n]]]][[2, 1]] (* JeanFrançois Alcover, Nov 26 2013 *)


PROG

(PARI) A115569_row(n)={if(n, my(u=vectorv(n, i, 10^i)\10, S=List(), M); forvec(v=vector(n, i, [1, 9]), (M=lcm(v))%10==0normlp(v, 1)%3^valuation(M, 3)for(k=1, n!, vecextract(v, numtoperm(n, k))*u%M listput(S, vecextract(v, numtoperm(n, k))*u)), 2); Set(S), concat(apply(A115569_row, [1..7])))} \\ Return terms of length n if given, else the vector of all terms. The checks M%10 and v % 3^v(...) are not needed but reduce CPU time by 97%.  M. F. Hasler, Jan 31 2016
(PARI) A115569(n)=n>9&&for(r=2, 7, (n=#t=A115569_row(r))>9return(t[n9+#t])); n \\ M. F. Hasler, Jan 31 2016


CROSSREFS

Cf. A034838, A034709, A063527.
Cf. A117911, A117912 (have even digits only), A117913 (have odd digits only), A010784.
Sequence in context: A002271 A048381 A185186 * A064653 A130588 A079238
Adjacent sequences: A115566 A115567 A115568 * A115570 A115571 A115572


KEYWORD

base,easy,nonn,fini,full


AUTHOR

Mike Smith (mtm_king(AT)yahoo.com), Mar 10 2006; also submitted by Andy Edwards (AndynGen(AT)aol.com), Mar 20 2006


EXTENSIONS

The full list of terms was sent in by Rick L. Shepherd (see link) and also by Sébastien Dumortier, Apr 04 2006


STATUS

approved



