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A153734 Triangle T(n,k): T(n,k) gives the A153452(m_k) such that A056239(m_k) = n, [1<=k<=A000041(n)], sorted by m_k, read by rows. Sequence A060240 is this sequence's permutation. 4
1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 3, 1, 1, 4, 5, 5, 6, 4, 1, 1, 9, 5, 5, 5, 10, 16, 9, 10, 5, 1, 1, 6, 14, 14, 35, 15, 21, 21, 14, 20, 35, 14, 15, 6, 1, 1, 7, 20, 14, 21, 28, 56, 64, 70, 42, 14, 90, 35, 70, 56, 28, 35, 64, 20, 21, 7, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Lengths of rows are 1, 1, 2, 3, 5, 7, 11, 15, 22, 30,.... (A000041). Row sums give A000085.

LINKS

Alois P. Heinz, Rows n = 0..26, flattened

EXAMPLE

For n=4, A056239(7) = A056239(9) = A056239(10) = A056239(12) = A056239(16) = 4. Hence T(4,k) = A153452(m_k) = (1,2,3,3,1), where 1<=k<=5, m_k = 7,9,10,12,16.

Triangle T(n,k) begins:

1;

1;

1, 1;

1, 2, 1;

1, 2, 3, 3, 1;

1, 4, 5, 5, 6,  4,  1;

1, 9, 5, 5, 5, 10, 16, 9, 10, 5, 1;

MAPLE

with(numtheory):

g:= proc(n) option remember; `if`(n=1, 1,

      add(g(n/q*`if`(q=2, 1, prevprime(q))), q=factorset(n)))

    end:

b:= proc(n, i) option remember; `if`(n=0 or i<2, [2^n],

       [seq(map(p->p*ithprime(i)^j, b(n-i*j, i-1))[], j=0..n/i)])

    end:

T:= n-> map(g, sort(b(n, n)))[]:

seq(T(n), n=0..10);  # Alois P. Heinz, Aug 09 2012

CROSSREFS

Cf. A067924, A215366.

Sequence in context: A253240 A290472 A060240 * A285554 A128495 A113136

Adjacent sequences:  A153731 A153732 A153733 * A153735 A153736 A153737

KEYWORD

easy,nonn,look,tabf

AUTHOR

Naohiro Nomoto, Dec 31 2008

STATUS

approved

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Last modified October 16 23:12 EDT 2018. Contains 316275 sequences. (Running on oeis4.)