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A238966 The number of distinct primes in divisor lattice in canonical order. 1
0, 1, 1, 2, 1, 2, 3, 1, 2, 2, 3, 4, 1, 2, 2, 3, 3, 4, 5, 1, 2, 2, 3, 2, 3, 4, 3, 4, 5, 6, 1, 2, 2, 3, 2, 3, 4, 3, 3, 4, 5, 4, 5, 6, 7, 1, 2, 2, 3, 2, 3, 4, 2, 3, 3, 4, 5, 3, 4, 4, 5, 6, 4, 5, 6, 7, 8, 1, 2, 2, 3, 2, 3, 4, 2, 3, 3, 4, 5, 3, 3, 4, 4, 5, 6, 3, 4, 5, 4, 5, 6, 7, 5, 6, 7, 8, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..2713 (rows 0..20)

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 [math.NT], 2014.

FORMULA

T(n,k) = A001221(A063008(n,k)). - Andrew Howroyd, Mar 25 2020

EXAMPLE

Triangle T(n,k) begins:

  0;

  1;

  1, 2;

  1, 2, 3;

  1, 2, 2, 3, 4;

  1, 2, 2, 3, 3, 4, 5;

  1, 2, 2, 3, 2, 3, 4, 3, 4, 5, 6;

  ...

MAPLE

o:= proc(n) option remember; nops(ifactors(n)[2]) end:

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-> o(mul(ithprime(i)^x[i], i=1..nops(x))), b(n$2))[]:

seq(T(n), n=0..9);  # Alois P. Heinz, Mar 26 2020

PROG

(PARI)

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

{ for(n=0, 8, print(Row(n))) } \\ Andrew Howroyd, Mar 25 2020

CROSSREFS

Row sums are A006128.

Cf. A036043 in canonical order.

Cf. A001221, A063008.

Sequence in context: A252230 A036043 A128628 * A275723 A198338 A199086

Adjacent sequences:  A238963 A238964 A238965 * A238967 A238968 A238969

KEYWORD

nonn,tabf,changed

AUTHOR

Sung-Hyuk Cha, Mar 07 2014

EXTENSIONS

Offset changed and terms a(50) and beyond from Andrew Howroyd, Mar 25 2020

STATUS

approved

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)