A083164 Rearrangement of natural numbers such that n divides sum of the terms with index which are the divisors of n.

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

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.

Links

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

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)

Crossrefs

Cf. A083165, A083166.

Sequence in context: A265355 A265354 A265356 * A094962 A338243 A338246

Adjacent sequences: A083161 A083162 A083163 * A083165 A083166 A083167

Keyword

nonn,look

Author

Amarnath Murthy, Apr 25 2003

Extensions

More terms from David Wasserman, Oct 22 2004

Status

approved