A306010
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 number m when the sums S(m) are arranged in increasing order.
Original entry on oeis.org
1, 2, 3, 4, 5, 7, 8, 6, 9, 11, 10, 13, 12, 16, 17, 15, 14, 19, 20, 18, 23, 21, 25, 27, 24, 22, 29, 28, 31, 32, 26, 33, 37, 35, 36, 41, 40, 34, 43, 30, 39, 47, 44, 45, 38, 49, 53, 48, 52, 51, 46, 55, 56, 59, 42, 61, 50, 57, 64, 63, 67, 54, 65, 71, 68, 58, 73
Offset: 1
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 terms of (a(n)) are 1,2,3,4,5,7,8,6.
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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 *)
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.
Original entry on oeis.org
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
Offset: 1
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.
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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 *)
A306013
Let P(m) be the product of unitary divisors of m; then a(n) is the position of P(n) when all the numbers P(m) are arranged in increasing order.
Original entry on oeis.org
1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 36, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 100, 144, 196, 225, 324, 400, 441, 484, 576, 676, 784, 1089, 1156, 1225, 1296, 1444, 1521, 1600, 1936, 2025, 2116
Offset: 1
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z = 100; r[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &];
k[n_] := Length[r[n]];
Table[r[n], {n, 1, z}]
a[n_] := Apply[Times, r[n]]
u = Table[a[n], {n, 1, z}]
Sort[u]
Showing 1-3 of 3 results.
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