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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
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
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
KEYWORD
nonn,tabl
AUTHOR
Rémy Sigrist, Sep 22 2018
STATUS
approved