A393812 Irregular triangle read by rows; integers with identical sigma values occurring at least twice, rows ordered by their smallest term.

6, 11, 10, 17, 14, 15, 23, 16, 25, 20, 26, 41, 21, 31, 24, 38, 59, 28, 39, 30, 46, 51, 55, 71, 33, 35, 47, 34, 53, 40, 58, 89, 42, 62, 69, 77, 44, 65, 83, 48, 75, 52, 97, 54, 56, 87, 95, 57, 79, 60, 78, 92, 123, 143, 167, 63, 103, 66, 70, 94, 115, 119, 68, 82

Offset

1,1

Comments

This sequence is a permutation of A206036.

The row length equals the number of occurrences of the corresponding sigma value (see A007609).

Each row contains at most one prime. If a prime p appears in a row, the row length equals A066075(A000720(p)).

Links

Felix Huber, Rows 1 to 1601, flattened

Example

6 and 11 are in a row since sigma(6) = sigma(11) = 12.
30, 46, 51, 55 and 71 are in a row since sigma(30) = sigma(46) = sigma(51) = sigma(55) = sigma(71) = 72.
The triangle begins:
    6   11
   10   17
   14   15   23
   16   25
   20   26   41
   21   31
   24   38   59
   28   39
   30   46   51   55   71
   33   35   47
   34   53
   40   58   89
   42   62   69   77
   44   65   83
   48   75
   52   97
   54   56   87   95
   57   79
   60   78   92  123  143  167
   63  103
   66   70   94  115  119
   68   82

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 := 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:
A393812 := proc(N) local i; seq(op(i), i in L(N)) end proc:
A393812(68); L(68); T(68);

Crossrefs

Cf. A000203, A007609, A066075, A206036, A211656, A392774.

Sequence in context: A134012 A103704 A135998 * A242825 A358068 A276136

Adjacent sequences: A393809 A393810 A393811 * A393813 A393814 A393815

Keyword

tabf,nonn

Author

Felix Huber, Mar 03 2026

Status

approved