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A167234 Smallest number such that no two divisors of n are congruent modulo a(n). 1
1, 2, 3, 4, 3, 6, 4, 5, 5, 6, 3, 7, 5, 8, 8, 9, 3, 10, 4, 7, 8, 6, 3, 13, 7, 7, 5, 11, 3, 11, 4, 9, 7, 6, 8, 13, 5, 5, 7, 11, 3, 16, 4, 12, 13, 6, 3, 17, 5, 11, 9, 7, 3, 10, 7, 15, 5, 5, 3, 21, 7, 7, 11, 11, 7, 14, 4, 7, 7, 16, 3, 13, 5, 10, 13, 7, 8, 14, 4, 17, 7, 6, 3, 23, 9, 8, 5, 13, 3, 19, 8, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

What can we say about the asymptotic behavior of this sequence? Does it contain every integer > 2 infinitely often?

For n > 6, a(n) <= floor(n/2) + 1; but this seems to be a very crude estimate.

LINKS

Paul Tek, Table of n, a(n) for n = 1..10000

PROG

(PARI) alldiff(v)=v=vecsort(v); for(k=1, #v-1, if(v[k]==v[k+1], return(0))); 1

a(n)=local(ds); ds=divisors(n); for(k=#ds, n, if(alldiff(vector(#ds, i, ds[i]%k)), return(k)))

CROSSREFS

Sequence in context: A079065 A097272 A126630 * A088043 A248376 A138796

Adjacent sequences:  A167231 A167232 A167233 * A167235 A167236 A167237

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, Oct 31 2009

STATUS

approved

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Last modified August 20 17:25 EDT 2017. Contains 290837 sequences.