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.

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

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