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

Offset: 0

Author

Amarnath Murthy, Aug 28 2002

Keywords

• nonn
• look
• tabf

Examples

			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:
  1;
  2;
  3,  4;
  4,  6,  8;
  5,  8,  9, 12, 16;
  6, 10, 12, 16, 18, 24, 32;
  ...
(End)
		

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.

Crossrefs

Row sums give A074141.

Cf. A036035, A074140.

Programs

PARI

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

Formula

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

Extensions

More terms from Alford Arnold, Sep 17 2002

Term ordering corrected by Alois P. Heinz, Aug 21 2019