A255483 -id:A255483 - cp's OEIS frontend

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

N. J. A. Sloane, Feb 16 2013

			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
........

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.

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

Similar array with primes in the starting row is A255483.

# 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))];

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 *)

A276579 Squarefree numbers larger than one for which A268669(A048675(n)) is a power of two.

Original entry on oeis.org

2, 3, 5, 6, 7, 10, 11, 13, 15, 17, 19, 21, 22, 23, 29, 31, 35, 37, 39, 41, 43, 46, 47, 53, 55, 59, 61, 67, 71, 73, 77, 79, 83, 85, 87, 89, 91, 97, 101, 103, 107, 109, 113, 118, 127, 131, 133, 137, 139, 143, 149, 151, 155, 157, 163, 167, 173, 179, 181, 183, 187, 191, 193, 197, 199, 210, 211, 221, 223, 227, 229, 233

Offset: 1

Antti Karttunen, Sep 18 2016

nonn

Terms present in arrays A255483 & A276578, sorted into ascending order.

Antti Karttunen, Table of n, a(n) for n = 1..2000

Cf. A000120, A008683, A008966, A048675, A209229, A268669.
Cf. array A255483 (A276578).
Subsequence of A005117.
A000040 is a subsequence.

A255484 a(n) = Product_{k=0..n} prime(k+1)*(binomial(n,k) mod 2).

Original entry on oeis.org

2, 6, 0, 210, 0, 0, 0, 9699690, 0, 0, 0, 0, 0, 0, 0, 32589158477190044730, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 525896479052627740771371797072411912900610967452630, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

N. J. A. Sloane, Feb 28 2015

nonn

A123098 is a much better version of this sequence.

Chai Wah Wu, Table of n, a(n) for n = 0..510

Cf. A123098, A255483.

f:=n->mul(ithprime(k+1)*(binomial(n,k) mod 2),k=0..n);
[seq(f(n),n=0..60)];

from operator import mul
from functools import reduce
from sympy import prime
def A255484(n):
    return reduce(mul,(0 if ~n & k else prime(k+1) for k in range(n+1))) # Chai Wah Wu, Feb 09 2016

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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.

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A276579 Squarefree numbers larger than one for which A268669(A048675(n)) is a power of two.

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A255484 a(n) = Product_{k=0..n} prime(k+1)*(binomial(n,k) mod 2).

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