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A059896 Table a(i,j) = product prime(k)^(Ei(k) OR Ej(k)) where Ei and Ej are the vectors of exponents in the prime factorizations of i and j; OR is the bitwise operation on binary representation of the exponents. 22
1, 2, 2, 3, 2, 3, 4, 6, 6, 4, 5, 8, 3, 8, 5, 6, 10, 12, 12, 10, 6, 7, 6, 15, 4, 15, 6, 7, 8, 14, 6, 20, 20, 6, 14, 8, 9, 8, 21, 24, 5, 24, 21, 8, 9, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10, 11, 10, 27, 8, 35, 6, 35, 8, 27, 10, 11, 12, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 12, 13, 24 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Analogous to LCM, with OR replacing MAX.

A003418-analog seems to be A066616. - Antti Karttunen, Apr 12 2017

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of the array

FORMULA

From Antti Karttunen, Apr 11 2017: (Start)

A(x,y) = A059895(x,y) * A059897(x,y).

A(x,y) * A059895(x,y) = x*y.

(End).

EXAMPLE

A(864,1944) = A(2^5*3^3,2^3*3^5) = 2^(5 OR 3) * 3^(3 OR 5) = 2^7*3^7 = 279936.

The top left 12 X 12 corner of the array:

   1,  2,  3,  4,  5,  6,  7,  8,   9,  10,  11,  12

   2,  2,  6,  8, 10,  6, 14,  8,  18,  10,  22,  24

   3,  6,  3, 12, 15,  6, 21, 24,  27,  30,  33,  12

   4,  8, 12,  4, 20, 24, 28,  8,  36,  40,  44,  12

   5, 10, 15, 20,  5, 30, 35, 40,  45,  10,  55,  60

   6,  6,  6, 24, 30,  6, 42, 24,  54,  30,  66,  24

   7, 14, 21, 28, 35, 42,  7, 56,  63,  70,  77,  84

   8,  8, 24,  8, 40, 24, 56,  8,  72,  40,  88,  24

   9, 18, 27, 36, 45, 54, 63, 72,   9,  90,  99, 108

  10, 10, 30, 40, 10, 30, 70, 40,  90,  10, 110, 120

  11, 22, 33, 44, 55, 66, 77, 88,  99, 110,  11, 132

  12, 24, 12, 12, 60, 24, 84, 24, 108, 120, 132,  12

MATHEMATICA

a[i_, i_] := i;

a[i_, j_] := Module[{f1 = FactorInteger[i], f2 = FactorInteger[j], e1, e2}, e1[_] = 0; Scan[(e1[#[[1]]] = #[[2]])&, f1]; e2[_] = 0; Scan[(e2[#[[1]]] = #[[2]])&, f2]; Times @@ (#^BitOr[e1[#], e2[#]]& /@ Union[f1[[All, 1]], f2[[All, 1]]])];

Table[a[i - j + 1, j], {i, 1, 15}, {j, 1, i}] // Flatten (* Jean-Fran├žois Alcover, Jun 19 2018 *)

PROG

(Scheme)

(define (A059896 n) (A059896bi (A002260 n) (A004736 n)))

(define (A059896bi a b) (let loop ((a a) (b b) (m 1)) (cond ((= 1 a) (* m b)) ((= 1 b) (* m a)) ((equal? (A020639 a) (A020639 b)) (loop (A028234 a) (A028234 b) (* m (expt (A020639 a) (A003986bi (A067029 a) (A067029 b)))))) ((< (A020639 a) (A020639 b)) (loop (/ a (A028233 a)) b (* m (A028233 a)))) (else (loop a (/ b (A028233 b)) (* m (A028233 b)))))))

;; Antti Karttunen, Apr 11 2017

CROSSREFS

Cf. A003418, A003986, A003990, A028233, A028234, A059895, A059897, A066616, A267116, A284576.

Sequence in context: A003990 A287958 A308630 * A079542 A220370 A291048

Adjacent sequences:  A059893 A059894 A059895 * A059897 A059898 A059899

KEYWORD

base,easy,nonn,tabl

AUTHOR

Marc LeBrun, Feb 06 2001

STATUS

approved

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Last modified February 24 13:13 EST 2021. Contains 341569 sequences. (Running on oeis4.)