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A286101 Square array A(n,k) read by antidiagonals: A(n,k) = T(gcd(n,k), lcm(n,k)), where T(n,k) is sequence A000027 considered as a two-dimensional table. 8
1, 2, 2, 4, 5, 4, 7, 16, 16, 7, 11, 12, 13, 12, 11, 16, 46, 67, 67, 46, 16, 22, 23, 106, 25, 106, 23, 22, 29, 92, 31, 191, 191, 31, 92, 29, 37, 38, 211, 80, 41, 80, 211, 38, 37, 46, 154, 277, 379, 436, 436, 379, 277, 154, 46, 56, 57, 58, 59, 596, 61, 596, 59, 58, 57, 56, 67, 232, 436, 631, 781, 862, 862, 781, 631, 436, 232, 67, 79, 80, 529, 212, 991, 302, 85, 302, 991, 212, 529, 80, 79 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The array is read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10585; the first 145 antidiagonals of array

MathWorld, Pairing Function

FORMULA

A(n,k) = T(gcd(n,k), lcm(n,k)), where T(n,k) is sequence A000027 considered as a two-dimensional table, that is, as a pairing function from N x N to N.

A(n,k) = A(k,n), or equivalently, a(A038722(n)) = a(n). [Array is symmetric.]

EXAMPLE

The top left 12 X 12 corner of the array:

   1,   2,   4,   7,   11,   16,   22,   29,   37,   46,   56,   67

   2,   5,  16,  12,   46,   23,   92,   38,  154,   57,  232,   80

   4,  16,  13,  67,  106,   31,  211,  277,   58,  436,  529,   94

   7,  12,  67,  25,  191,   80,  379,   59,  631,  212,  947,  109

  11,  46, 106, 191,   41,  436,  596,  781,  991,   96, 1486, 1771

  16,  23,  31,  80,  436,   61,  862,  302,  193,  467, 2146,  142

  22,  92, 211, 379,  596,  862,   85, 1541, 1954, 2416, 2927, 3487

  29,  38, 277,  59,  781,  302, 1541,  113, 2557,  822, 3829,  355

  37, 154,  58, 631,  991,  193, 1954, 2557,  145, 4006, 4852,  706

  46,  57, 436, 212,   96,  467, 2416,  822, 4006,  181, 5996, 1832

  56, 232, 529, 947, 1486, 2146, 2927, 3829, 4852, 5996,  221, 8647

  67,  80,  94, 109, 1771,  142, 3487,  355,  706, 1832, 8647,  265

PROG

(Scheme)

(define (A286101 n) (A286101bi (A002260 n) (A004736 n)))

(define (A286101bi row col) (A000027bi (gcd row col) (lcm row col)))

(define (A000027bi row col) (* (/ 1 2) (+ (expt (+ row col) 2) (- row) (- (* 3 col)) 2)))

CROSSREFS

Cf. A000124 (row 1 and column 1), A001844 (main diagonal).

Cf. A000027, A003989, A003990, A003991, A038722, A285722, A285732, A286098, A286099, A286102, A285724.

Sequence in context: A136099 A210597 A252836 * A072454 A115216 A208637

Adjacent sequences:  A286098 A286099 A286100 * A286102 A286103 A286104

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, May 03 2017

STATUS

approved

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Last modified June 12 09:24 EDT 2021. Contains 344946 sequences. (Running on oeis4.)