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A305995
Rectangular array read by downward antidiagonals; row n consists of the numbers m such that n is the denominator of d(k)/d(1) + d(k-1)/d(2) + ... + d(k)/d(1), where d(1),d(2),...,d(k) are the unitary divisors of m.
6
1, 10, 2, 65, 68, 3, 130, 520, 6, 4, 260, 1768, 15, 40, 5, 340, 2600, 30, 104, 50, 12, 1105, 6760, 60, 1040, 1700, 120, 7, 1972, 17680, 150, 20560, 3250, 312, 14, 8, 2210, 62600, 195, 35360, 7825, 600, 35, 2080, 9, 4420, 165896, 204, 85280, 27625, 3120, 70, 4112, 18, 20
OFFSET
1,2
COMMENTS
Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers. The numbers in row n are divisible by n; see A305996 for the quotients.
EXAMPLE
Northwest corner:
1 10 65 130 260 340 1105
2 68 520 1768 2600 6760 17680
3 6 15 30 60 150 195
4 40 104 1040 20560 35360 85280
5 50 1700 3250 7825 27625 31300
12 120 312 600 3120 61680 106080
7 14 35 70 140 175 350
8 2080 4112 6560 32800 38048 52000
9 18 90 369 585 612 738
MATHEMATICA
t[n_] := Table[r[n][[k[n] + 1 - i]]/r[n][[k[1] + i - 1]], {i, 1, k[n]}];
s = Table[Total[t[n]], {n, 1, z}]; a[n_] := If[IntegerQ[s[[n]]], 1, 0];
d = Denominator[s];
row[n_] := Flatten[Position[d, n]]
TableForm[Table[row[n], {n, 1, 10}]] (* A305995 array *)
r1[n_, k_] := row[n][[k]]; zz = 10;
Flatten[Table[r1[n - k + 1, k], {n, zz}, {k, n, 1, -1}]] (* A305995 sequence *)
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jun 16 2018
STATUS
approved