A077351 Smallest multiple of n using all the digits of all its divisors (a permutation of the concatenation of its divisors), or 0 if no such number exists.

1, 12, 0, 124, 15, 1236, 0, 1248, 0, 11250, 0, 0, 0, 21714, 11355, 112864, 0, 0, 0, 10122540, 0, 0, 0, 1122234648, 1525, 112632, 0, 11242784, 0, 10112335560, 0, 11223648, 0, 131274, 13755, 0, 0, 123918, 0, 10012245480, 0, 11122234746, 0

Offset: 1

Author

Amarnath Murthy, Nov 05 2002

Keywords

• base
• nonn

Comments

For a list of all values of n up to 10000 where a(n)=0, see A179197. - Jon E. Schoenfield, Jul 10 2010

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A077352, A179197.

Programs

Maple

A077351 := proc(n) local ndvs,ds,d,m,muldivs ; ndvs := [] ; ds := numtheory[divisors](n) ; for d from 1 to nops(ds) do ndvs := [op(ndvs), op(convert(op(d,ds),base,10))]; od ; ndvs := sort(ndvs) ; m := floor( 10^(nops(ndvs)-1)/n) ; while m*n < op(-1,ndvs)*10^(nops(ndvs)-1) do muldivs := sort(convert(m*n,base,10)) ; if muldivs = ndvs then RETURN(m*n) ; fi ; m := m+1 ; od ; RETURN(0) ; end: for n from 1 to 25 do print(n,A077351(n)) ; od ; # R. J. Mathar, Mar 20 2007

Extensions

Corrected and extended by R. J. Mathar, Mar 20 2007

a(24) from Don Reble, Nov 07 2007; a(25)-a(29) from R. J. Mathar, Mar 20 2007

More terms from Jon E. Schoenfield, Jul 02 2010