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A306011 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 numerator of S(m)  when the all the numbers S(m) are arranged in increasing order. 4
1, 5, 10, 17, 26, 50, 65, 25, 82, 122, 13, 170, 85, 257, 290, 52, 125, 362, 221, 205, 530, 500, 626, 730, 325, 305, 842, 425, 962, 1025, 425, 1220, 1370, 260, 697, 1682, 169, 725, 1850, 130, 1700, 2210, 1037, 2132, 905, 2402, 2810, 1285, 1445, 2900, 1325 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..51.

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 numerators are 1,5,10,17,26,50,65,25.

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, A306012.

Sequence in context: A098749 A034676 A076598 * A080341 A271328 A086653

Adjacent sequences:  A306008 A306009 A306010 * A306012 A306013 A306014

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 16 2018

STATUS

approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)