OFFSET
1,1
COMMENTS
A positive integer does not appear if its (tau, sigma) pair is unique.
LINKS
Felix Huber, Rows 1 to 2662, flattened
EXAMPLE
14 and 15 are in a row since tau(14) = tau(15) = 4 and sigma(14) = sigma(15) = 24.
46, 51 and 55 are in a row since tau(46) = tau(51) = tau(55) = 4 and sigma(46) = sigma(51) = sigma(55) = 72.
16 is not in the sequence because its (tau, sigma) pair (5, 31) is unique.
The triangle begins:
14 15
33 35
46 51 55
54 56
62 69 77
66 70
87 95
94 115 119
102 110
114 135
118 145
123 143
132 140
138 154 165
141 155 161
142 159 187
158 177 203 209
166 205 221
174 184 190
182 195
186 231
204 220 224
213 235 253
MAPLE
with(NumberTheory):
L := proc(N) # All rows with smallest number <= N
local t, k, d, i, m;
m := max(seq(sigma(k), k = 1 .. N)) - 1;
t := table();
for k to m do
d := [tau(k), sigma(k)];
if assigned(t[d]) then
t[d] := [op(t[d]), k]
else
t[d] := [k]
end if
end do;
sort([seq(`if`(nops(t[op(i)]) > 1 and t[op(i)][1] <= N, t[op(i)], NULL), i in indices(t))], (x, y) -> x[1] < y[1]);
end proc:
T := proc(N) local l, w, i, j; l := L(N); w := 0; for i in l do for j to nops(i) do w := max(w, length(convert(i[j], string))); end do; end do; w := w + 2; for i in l do for j to nops(i) do printf(cat("%", w, "d"), i[j]); end do; printf("\n"); end do; end proc:
A392774 := proc(N) local i; seq(op(i), i in L(N)) end proc:
A392774(213); L(213); T(213);
CROSSREFS
KEYWORD
tabf,nonn
AUTHOR
Felix Huber, Mar 03 2026
STATUS
approved
