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A238963 Number of divisors of A063008(n,k). 4
1, 2, 3, 4, 4, 6, 8, 5, 8, 9, 12, 16, 6, 10, 12, 16, 18, 24, 32, 7, 12, 15, 20, 16, 24, 32, 27, 36, 48, 64, 8, 14, 18, 24, 20, 30, 40, 32, 36, 48, 64, 54, 72, 96, 128, 9, 16, 21, 28, 24, 36, 48, 25, 40, 45, 60, 80, 48, 64, 72, 96, 128, 81, 108, 144, 192, 256, 10, 18, 24, 32, 28, 42, 56, 30, 48, 54, 72, 96, 50, 60, 80, 90, 120, 160, 64, 96, 128, 108, 144, 192, 256, 162, 216, 288, 384, 512 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equivalent to A074139 but using canonical order.

LINKS

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

S.-H. Cha, E. G. DuCasse, and L. V. Quintas, Graph Invariants Based on the Divides Relation and Ordered by Prime Signatures, arxiv:1405.5283

FORMULA

T(n, k) = A000005(A063008(n,k)).

EXAMPLE

Triangle begins:

  1;

  2;

  3,  4;

  4,  6,  8;

  5,  8,  9, 12, 16;

  6, 10, 12, 16, 18, 24, 32;

  7, 12, 15, 20, 16, 24, 32, 27, 36, 48, 64;

  ...

MAPLE

b:= (n, i)-> `if`(n=0 or i=1, [[1$n]], [map(x->

    [i, x[]], b(n-i, min(n-i, i)))[], b(n, i-1)[]]):

T:= n-> map(x-> numtheory[tau](mul(ithprime(i)

        ^x[i], i=1..nops(x))), b(n$2))[]:

seq(T(n), n=0..9);  # Alois P. Heinz, Mar 24 2020

PROG

(PARI) \\ here b(n) is A000005.

b(n)={numdiv(n)}

N(sig)={prod(k=1, #sig, prime(k)^sig[k])}

Row(n)={apply(s->b(N(s)), vecsort([Vecrev(p) | p<-partitions(n)], , 4))}

{ for(n=0, 8, print(Row(n))) } \\ Andrew Howroyd, Mar 24 2020

CROSSREFS

Row sums are A074141.

Cf. A000005, A000041, A063008, A074139.

Sequence in context: A325682 A241088 A074139 * A342940 A331527 A326575

Adjacent sequences:  A238960 A238961 A238962 * A238964 A238965 A238966

KEYWORD

nonn,tabf

AUTHOR

Sung-Hyuk Cha, Mar 07 2014

EXTENSIONS

Offset corrected by Andrew Howroyd, Mar 24 2020

STATUS

approved

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)