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A074139 Number of divisors of A036035(n,k). 18
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:

  1;

  2;

  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.

Cf. A036035, A074140.

Sequence in context: A007896 A325682 A241088 * A238963 A331527 A326575

Adjacent sequences:  A074136 A074137 A074138 * A074140 A074141 A074142

KEYWORD

nonn,look,tabf

AUTHOR

Amarnath Murthy, Aug 28 2002

EXTENSIONS

More terms from Alford Arnold, Sep 17 2002

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

STATUS

approved

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Last modified September 22 10:23 EDT 2020. Contains 337289 sequences. (Running on oeis4.)