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%I #43 Jun 26 2017 07:58:22
%S 1,1,1,2,5,1,1,1,1,3,3,2,2,9,2,2,9,7,8,6,6,33,256,1,1,1,1,26,5,1,1,1,
%T 1,149,24,4,159,4,130,3,3,3,3,118,16,128,16,3,3,3,3,14,16,16,840,13,
%U 89,15,88,2,2,12,2,2,78,11,13,76,597,12,71,2,2,555,2
%N a(n) = least k > 0 such that k * n in factorial base representation contains only 0's and 1's.
%C a(n) = 1 iff n belongs to A059590.
%C a(a(n)) <= n for any n > 0.
%H Rémy Sigrist, <a href="/A284750/b284750.txt">Table of n, a(n) for n = 1..2000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Factorial_number_system">Factorial number system</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F a(n) = A286820(n) / n.
%e The first terms, alongside n*a(n) in decimal and factorial base, are:
%e n a(n) n*a(n) n*a(n) in factorial base
%e -- ---- ------ ------------------------
%e 1 1 1 1
%e 2 1 2 1,0
%e 3 1 3 1,1
%e 4 2 8 1,1,0
%e 5 5 25 1,0,0,1
%e 6 1 6 1,0,0
%e 7 1 7 1,0,1
%e 8 1 8 1,1,0
%e 9 1 9 1,1,1
%e 10 3 30 1,1,0,0
%e 11 3 33 1,1,1,1
%e 12 2 24 1,0,0,0
%e 13 2 26 1,0,1,0
%e 14 9 126 1,0,1,0,0
%e 15 2 30 1,1,0,0
%e 16 2 32 1,1,1,0
%e 17 9 153 1,1,1,1,1
%e 18 7 126 1,0,1,0,0
%e 19 8 152 1,1,1,1,0
%e 20 6 120 1,0,0,0,0
%o (PARI) isA059590(n) = my (r=2); while (n, if (n%r > 1, return (0), n\=r; r++)); return (1)
%o a(n) = for (k=1, oo, if (isA059590(k*n), return (k)))
%Y Cf. A059590, A286820.
%K nonn,base
%O 1,4
%A _Rémy Sigrist_, Jun 25 2017
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