A074139 - OEIS

A074139

Number of divisors of A036035(n,k).

1, 2, 3, 4, 4, 6, 8, 5, 8, 9, 12, 16, 6, 10, 12, 16, 18, 24, 32, 7, 12, 15, 16, 20, 24, 27, 32, 36, 48, 64, 8, 14, 18, 20, 24, 30, 32, 36, 40, 48, 54, 64, 72, 96, 128, 9, 16, 21, 24, 25, 28, 36, 40, 45, 48, 48, 60, 64, 72, 81, 80, 96, 108, 128, 144, 192, 256

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Alois P. Heinz, Rows n = 0..30, flattened

Byungchul Cha et al., An Investigation on Partitions with Equal Products, arXiv:1811.07451 [math.NT], 2018.

FORMULA

T(n,k) = A000005(A036035(n,k)). - R. J. Mathar, Aug 28 2018

EXAMPLE

Express A036035(n,k) by its prime signature; add one to each exponent, then multiply: 180 = (2^2)*(3^2)*(5^1) therefore the number of divisors is (2+1)*(2+1)*(1+1)= 18

From Michel Marcus, Nov 11 2015: (Start)

As an irregular triangle, whose n-th row has A000041(n) terms, sequence begins:

3, 4;

4, 6, 8;

5, 8, 9, 12, 16;

6, 10, 12, 16, 18, 24, 32;

...

(End)

PROG

(PARI) tabf(nn) = {for (n=1, nn, forpart(p=n, print1(prod(k=1, #p, (1+p[k])), ", ")); print(); ); } \\ Michel Marcus, Nov 11 2015

CROSSREFS

Row sums give A074141.