

A076084


Consider all numbers that can be formed by permuting the digits of n; take those with the greatest number of divisors; a(n) is the smallest of them.


2



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 91, 20, 12, 22, 32, 24, 52, 26, 72, 28, 92, 30, 13, 32, 33, 34, 35, 36, 37, 38, 39, 40, 14, 24, 34, 44, 54, 64, 74, 84, 94, 50, 15, 52, 35, 54, 55, 56, 75, 58, 95, 60, 16, 26, 36, 64, 56, 66, 76, 68, 96, 70, 17, 72
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OFFSET

1,2


LINKS



EXAMPLE

a(24)=a(42) = 24. a(61) = 16.
From the numbers found by permuting the digits 1138, we get 1138, 1183, 1318, 1381, 1813, 1831, 3118, 3181, 3811, 8113, 8131 and 8311. We find that 8113 has the most divisors of those, namely 8. Therefore a(1138) = 8113.  David A. Corneth, Apr 22 2016


MATHEMATICA

pdn[n_]:=Module[{c=SortBy[{#, DivisorSigma[0, #]}&/@FromDigits/@ Permutations[ IntegerDigits[n]], Last], m}, m=c[[1, 2]]; Min[Transpose[ Select[c, #[[2]]==m&]][[1]]]]; Array[pdn, 80] (* Harvey P. Dale, Nov 29 2013 *)


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STATUS

approved



