

A083164


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


3



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, 63, 24, 57, 14, 61, 32, 53, 31, 47, 66, 73, 35, 102, 52, 81, 43, 42, 84, 45, 112, 46, 56, 133, 90, 117, 74, 105, 99, 145, 48, 17, 55, 58, 60, 121, 59, 153, 64, 108, 93, 200, 132
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OFFSET

1,2


COMMENTS

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.


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EXAMPLE

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


PROG

(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)


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STATUS

approved



