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A306012 Let S(m) = d(k)/d(1) + ... + d(1)/d(k), where d(1)..d(k) are the unitary divisors of m; then a(n) is the denominator of S(m) when all the numbers S(m) are arranged in increasing order. 4
1, 2, 3, 4, 5, 7, 8, 3, 9, 11, 1, 13, 6, 16, 17, 3, 7, 19, 10, 9, 23, 21, 25, 27, 12, 11, 29, 14, 31, 32, 13, 33, 37, 7, 18, 41, 4, 17, 43, 3, 39, 47, 22, 45, 19, 49, 53, 24, 26, 51, 23, 55, 28, 59, 21, 61, 5, 57, 64, 63, 67, 27, 1, 71, 2, 29, 73, 3, 36, 69 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..70.

EXAMPLE

The first 8 pairs {m,S(m)} are {1, 1}, {2, 5/2}, {3, 10/3}, {4, 17/4}, {5, 26/5}, {6, 25/3}, {7, 50/7}, {8, 65/8}. When the numbers S(m) are arranged in increasing order, the pairs are {1, 1}, {2, 5/2}, {3, 10/3}, {4, 17/4}, {5, 26/5}, {7, 50/7}, {8, 65/8}, {6, 25/3}, so that the first 8 denominators are 1,2,3,4,5,7,8,3.

MATHEMATICA

z = 100; r[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &];

k[n_] := Length[r[n]];

t[n_] := Table[r[n][[k[n] + 1 - i]]/r[n][[k[1] + i - 1]], {i, 1, k[n]}];

s = Table[{n, Total[t[n]]}, {n, 1, z}]

v = SortBy[s, Last]

v1 = Table[v[[n]][[1]], {n, 1, z}]  (* A306010 *)

w = Table[v[[n]][[2]], {n, 1, z}];

Numerator[w]    (* A306011 *)

Denominator[w]  (* A306012 *)

CROSSREFS

Cf. A077610, A229994, A229996, A305995, A306010, A306011.

Sequence in context: A214921 A265566 A265550 * A082352 A122320 A123713

Adjacent sequences:  A306009 A306010 A306011 * A306013 A306014 A306015

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 16 2018

STATUS

approved

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Last modified September 23 11:33 EDT 2021. Contains 347612 sequences. (Running on oeis4.)