A319523 Square array T(n, k) (n >= 1, k >= 1) read by antidiagonals upwards: T(n, k) is the unique positive integer m such that A319521(m) = n and A319522(m) = k.

1, 2, 3, 5, 6, 7, 4, 15, 14, 9, 11, 12, 35, 18, 13, 10, 33, 28, 45, 26, 21, 17, 30, 77, 36, 65, 42, 19, 8, 51, 70, 99, 52, 105, 38, 27, 25, 24, 119, 90, 143, 84, 95, 54, 49, 22, 75, 56, 153, 130, 231, 76, 135, 98, 39, 23, 66, 175, 72, 221, 210, 209, 108, 245

Offset

1,2

Links

Table of n, a(n) for n=1..64.

Formula

T(n, k) = A061898(T(k, n)).

T(n, n) = A275407(n).

T(n, 1) = A319525(n).

T(1, k) = A297002(k).

T(n, k) = T(n, 1) * T(1, k) = A319525(n) * A297002(k).

A001221(T(n, k)) = A001221(n) + A001221(k).

A001222(T(n, k)) = A001222(n) + A001222(k).

Example

Array T(n, k) begins:
  n\k|    1    2    3    4    5    6    7    8    9   10   11   12
  ---+------------------------------------------------------------
    1|    1    3    7    9   13   21   19   27   49   39   29   63
    2|    2    6   14   18   26   42   38   54   98   78   58  126
    3|    5   15   35   45   65  105   95  135  245  195  145  315
    4|    4   12   28   36   52   84   76  108  196  156  116  252
    5|   11   33   77   99  143  231  209  297  539  429  319  693
    6|   10   30   70   90  130  210  190  270  490  390  290  630
    7|   17   51  119  153  221  357  323  459  833  663  493 1071
    8|    8   24   56   72  104  168  152  216  392  312  232  504
    9|   25   75  175  225  325  525  475  675 1225  975  725 1575
   10|   22   66  154  198  286  462  418  594 1078  858  638 1386

Prog

(PARI) T(n, k) = my (fn=factor(n), fk=factor(k)); prod(i=1, #fn~, prime(2*primepi(fn[i, 1])-1)^fn[i, 2]) * prod(i=1, #fk~, prime(2*primepi(fk[i, 1]))^fk[i, 2])

Crossrefs

Cf. A001221, A001222, A061898, A275407 (main diagonal), A297002 (first row), A319521, A319522, A319525 (first column).

Sequence in context: A367407 A354370 A113821 * A255367 A280098 A019517

Adjacent sequences: A319520 A319521 A319522 * A319524 A319525 A319526

Keyword

nonn,tabl

Author

Rémy Sigrist, Sep 22 2018

Status

approved