A286102 - OEIS

A286102

Square array A(n,k) read by antidiagonals: A(n,k) = T(lcm(n,k), gcd(n,k)), where T(n,k) is sequence A000027 considered as a two-dimensional table.

1, 3, 3, 6, 5, 6, 10, 21, 21, 10, 15, 14, 13, 14, 15, 21, 55, 78, 78, 55, 21, 28, 27, 120, 25, 120, 27, 28, 36, 105, 34, 210, 210, 34, 105, 36, 45, 44, 231, 90, 41, 90, 231, 44, 45, 55, 171, 300, 406, 465, 465, 406, 300, 171, 55, 66, 65, 64, 63, 630, 61, 630, 63, 64, 65, 66, 78, 253, 465, 666, 820, 903, 903, 820, 666, 465, 253, 78, 91, 90, 561, 230, 1035, 324, 85, 324, 1035, 230, 561, 90, 91

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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(lcm(n,k), gcd(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, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78

3, 5, 21, 14, 55, 27, 105, 44, 171, 65, 253, 90

6, 21, 13, 78, 120, 34, 231, 300, 64, 465, 561, 103

10, 14, 78, 25, 210, 90, 406, 63, 666, 230, 990, 117

15, 55, 120, 210, 41, 465, 630, 820, 1035, 101, 1540, 1830

21, 27, 34, 90, 465, 61, 903, 324, 208, 495, 2211, 148

28, 105, 231, 406, 630, 903, 85, 1596, 2016, 2485, 3003, 3570

36, 44, 300, 63, 820, 324, 1596, 113, 2628, 860, 3916, 375

45, 171, 64, 666, 1035, 208, 2016, 2628, 145, 4095, 4950, 739

55, 65, 465, 230, 101, 495, 2485, 860, 4095, 181, 6105, 1890

66, 253, 561, 990, 1540, 2211, 3003, 3916, 4950, 6105, 221, 8778

78, 90, 103, 117, 1830, 148, 3570, 375, 739, 1890, 8778, 265

PROG

(Scheme)

(define (A286102 n) (A286102bi (A002260 n) (A004736 n)))

(define (A286102bi row col) (A000027bi (lcm row col) (gcd row col)))

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

CROSSREFS

Cf. A000027, A003989, A003990, A003991, A038722, A285722, A285732, A286098, A286099, A286101, A285724.

Cf. A000217 (row 1 and column 1), A001844 (main diagonal).

Sequence in context: A142149 A132119 A180681 * A023822 A318514 A355413

Adjacent sequences: A286099 A286100 A286101 * A286103 A286104 A286105

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, May 03 2017

STATUS

approved