A278109 -id:A278109 - cp's OEIS frontend

A278110 a(n) = Product_{k=1..A056811(n)} A000040(k)^A278109(n,k).

1, 1, 1, 2, 2, 2, 2, 4, 12, 12, 12, 24, 24, 24, 24, 48, 48, 144, 144, 288, 288, 288, 288, 576, 2880, 2880, 8640, 17280, 17280, 17280, 17280, 34560, 34560, 34560, 34560, 207360, 207360, 207360, 207360, 414720, 414720, 414720, 414720, 829440, 2488320

Offset: 1

Jason Kimberley, Feb 02 2017

Jason Kimberley, Table of n, a(n) for n = 1..1000

Cf. A033833, A181817, A278108, A278109.

[&*[Integers()|p^(n div p^2):p in PrimesUpTo(Isqrt(n))]:n in[1..45]];

A278108 Irregular triangle read by rows: T(n,k) = floor(n/k^2) for 1 <= k^2 <= n.

Original entry on oeis.org

1, 2, 3, 4, 1, 5, 1, 6, 1, 7, 1, 8, 2, 9, 2, 1, 10, 2, 1, 11, 2, 1, 12, 3, 1, 13, 3, 1, 14, 3, 1, 15, 3, 1, 16, 4, 1, 1, 17, 4, 1, 1, 18, 4, 2, 1, 19, 4, 2, 1, 20, 5, 2, 1, 21, 5, 2, 1, 22, 5, 2, 1, 23, 5, 2, 1, 24, 6, 2, 1, 25, 6, 2, 1, 1, 26, 6, 2, 1, 1, 27, 6, 3, 1, 1, 28, 7, 3, 1, 1, 29, 7, 3, 1, 1

Offset: 1

Jason Kimberley, Feb 01 2017

The row length sequence is A000196.

			The first 27 rows are:
1;
2;
3;
4, 1;
5, 1;
6, 1;
7, 1;
8, 2;
9, 2, 1;
10, 2, 1;
11, 2, 1;
12, 3, 1;
13, 3, 1;
14, 3, 1;
15, 3, 1;
16, 4, 1, 1;
17, 4, 1, 1;
18, 4, 2, 1;
19, 4, 2, 1;
20, 5, 2, 1;
21, 5, 2, 1;
22, 5, 2, 1;
23, 5, 2, 1;
24, 6, 2, 1;
25, 6, 2, 1, 1;
26, 6, 2, 1, 1;
27, 6, 3, 1, 1;

Jason Kimberley, Table of n, a(n) for n = 1..20615 (the first 1000 rows of the triangle)

Cf. A000196, A010766, A277646, A277647, A278109.

[n div k^2:k in[1..Isqrt(n)],n in[1..27]];

cp's OEIS Frontend

A278110 a(n) = Product_{k=1..A056811(n)} A000040(k)^A278109(n,k).

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