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Rearrangement of natural numbers such that n divides sum of the terms with index which are the divisors of n.
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%I #15 Apr 17 2015 15:23:06

%S 1,3,2,4,9,6,13,8,15,7,10,20,12,11,18,16,33,27,37,36,5,30,22,28,40,62,

%T 63,24,57,14,61,32,53,31,47,66,73,35,102,52,81,43,42,84,45,112,46,56,

%U 133,90,117,74,105,99,145,48,17,55,58,60,121,59,153,64,108,93,200,132

%N Rearrangement of natural numbers such that n divides sum of the terms with index which are the divisors of n.

%C a(n) = (smallest multiple larger than the sum of the terms with index which are the divisors (<n) of n) - (The sum of the terms with index which are the divisors ( <n ) of n) if the resulting number is not already included, else go for the next larger multiple.

%H Paul Tek, <a href="/A083164/b083164.txt">Table of n, a(n) for n = 1..10000</a>

%e 9 divides a(1) + a(3) + a(9) = 1 + 2 + 15 = 18.

%o (PARI) A = vector(105); used = vector(400); for (n = 1, 105, d = divisors(n); c = numdiv(n); s = 0; for (i = 1, c - 1, s += A[d[i]]); x = n - s%n; while (used[x], x += n); A[n] = x; used[x] = 1; write("a083165.txt", (x + s)/n)); write("a083164.txt", A)

%Y Cf. A083165, A083166.

%K nonn,look

%O 1,2

%A _Amarnath Murthy_, Apr 25 2003

%E More terms from _David Wasserman_, Oct 22 2004