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A222310 Array read by antidiagonals: first row is 1, 2, 3, 4, ...; for subsequent rows, write i*j/gcd(i,j)^2 under ...i.j... in previous row. 4
1, 2, 2, 3, 6, 3, 6, 2, 12, 4, 5, 30, 15, 20, 5, 15, 3, 10, 6, 30, 6, 105, 7, 21, 210, 35, 42, 7, 70, 6, 42, 2, 420, 12, 56, 8, 1, 70, 105, 10, 5, 84, 63, 72, 9, 5, 5, 14, 30, 3, 15, 1260, 20, 90, 10, 33, 165, 33, 462, 385, 1155, 77, 1980, 99, 110, 11, 55, 15, 11, 3, 154, 10, 462, 6, 330, 30, 132, 12, 65, 143, 2145, 195, 65, 10010, 1001, 78 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..8001

Cristian Cobeli, Mihai Prunescu, Alexandru Zaharescu, A growth model based on the arithmetic Z-game, arXiv:1511.04315 [math.NT], 2015.

C. Cobeli and A. Zaharescu, Promenade around Pascal Triangle-Number Motives, Bull. Math. Soc. Sci. Math. Roumanie, Tome 56(104) No. 1, 2013, 73-98.

EXAMPLE

Array begins:

1...2...3.....4......5......6.....7.....8.....9.....10

..2...6....12....20.....30....42.....56...72.....90

....3...2....15......6.....35....12....63....20

......6....30....10....210...420.....84..1260

........5.....3.....21......2.....5....15

...........15.....7.....42....10......3

.............105.....6.....105...30

........

MAPLE

# To get first M rows of the array (s0 is A222311):

g:=(i, j)->i*j/gcd(i, j)^2;

M:=50;

s0:=[1]:

s1:=[seq(n, n=1..M)]:

for i1 from 1 to M-1 do

lprint(s1);

s2:=[seq(g(s1[i], s1[i+1]), i=1..nops(s1)-1)];

s0:=[op(s0), s2[1]];

s1:=[seq(s2[i], i=1..nops(s2))];

od:

# To produce A222310 (i.e., to read the array by antidiagonals):

g:=(i, j)->i*j/gcd(i, j)^2;

M:=15;

b1:=Array(1..M);

s0:=[1]:

s1:=[seq(n, n=1..M)]:

b1[1]:=s1;

for i1 from 1 to M-1 do

#lprint(s1);

s2:=[seq(g(s1[i], s1[i+1]), i=1..nops(s1)-1)];

b1[i1+1]:=s2;

s0:=[op(s0), s2[1]];

s1:=[seq(s2[i], i=1..nops(s2))];

od:

#[seq(s0[i], i=1..nops(s0))]; (that gives A222311)

lis:=[]:

for i from 1 to M do for j from 1 to i do

lis:=[op(lis), b1[i-j+1][j]];

od: od:

[seq(lis[k], k=1..nops(lis))];

MATHEMATICA

a = r = {1}; Do[a = Join[a, Reverse[r = FoldList[#1*#2/GCD[#1, #2]^2 &, n, r]]], {n, 2, 13}]; a (* Ivan Neretin, May 14 2015 *)

CROSSREFS

Cf. A036262. Leading diagonal is A222311 (cf. A222313).

Similar array with primes in the starting row is A255483.

Sequence in context: A210859 A209420 A317449 * A294033 A254827 A193862

Adjacent sequences:  A222307 A222308 A222309 * A222311 A222312 A222313

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Feb 16 2013

STATUS

approved

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Last modified February 25 04:32 EST 2020. Contains 332217 sequences. (Running on oeis4.)