cp's OEIS Frontend

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.

%I A319523 #9 Sep 24 2018 08:55:30
%S A319523 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,
%T A319523 65,42,19,8,51,70,99,52,105,38,27,25,24,119,90,143,84,95,54,49,22,75,
%U A319523 56,153,130,231,76,135,98,39,23,66,175,72,221,210,209,108,245
%N 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.
%F A319523 T(n, k) = A061898(T(k, n)).
%F A319523 T(n, n) = A275407(n).
%F A319523 T(n, 1) = A319525(n).
%F A319523 T(1, k) = A297002(k).
%F A319523 T(n, k) = T(n, 1) * T(1, k) = A319525(n) * A297002(k).
%F A319523 A001221(T(n, k)) = A001221(n) + A001221(k).
%F A319523 A001222(T(n, k)) = A001222(n) + A001222(k).
%e A319523 Array T(n, k) begins:
%e A319523   n\k|    1    2    3    4    5    6    7    8    9   10   11   12
%e A319523   ---+------------------------------------------------------------
%e A319523     1|    1    3    7    9   13   21   19   27   49   39   29   63
%e A319523     2|    2    6   14   18   26   42   38   54   98   78   58  126
%e A319523     3|    5   15   35   45   65  105   95  135  245  195  145  315
%e A319523     4|    4   12   28   36   52   84   76  108  196  156  116  252
%e A319523     5|   11   33   77   99  143  231  209  297  539  429  319  693
%e A319523     6|   10   30   70   90  130  210  190  270  490  390  290  630
%e A319523     7|   17   51  119  153  221  357  323  459  833  663  493 1071
%e A319523     8|    8   24   56   72  104  168  152  216  392  312  232  504
%e A319523     9|   25   75  175  225  325  525  475  675 1225  975  725 1575
%e A319523    10|   22   66  154  198  286  462  418  594 1078  858  638 1386
%o A319523 (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])
%Y A319523 Cf. A001221, A001222, A061898, A275407 (main diagonal), A297002 (first row), A319521, A319522, A319525 (first column).
%K A319523 nonn,tabl
%O A319523 1,2
%A A319523 _Rémy Sigrist_, Sep 22 2018