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A107329 Triangle read by rows: T(n,k) gives number of partitions of k,(k=1..n) into the prime factors of n. 0
0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,20

COMMENTS

T(n,n) equals A066882. Table begins at n=2 since 1 has no valid prime decomposition: {0, 1}, {0, 0, 1}, {0, 1, 0, 1}, {0, 0, 0, 0, 1}, {0, 1, 1, 1, 1, 2}, {0, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 1, 0, 1, 0, 1}, {0, 0, 1, 0, 0, 1, 0, 0, 1}

LINKS

Table of n, a(n) for n=2..106.

FORMULA

T(n, k) is factor of x^k in 1/Product( 1-x^p_i) with p_i the prime factors of n.

EXAMPLE

T(30,12)=5 counting [2,2,2,2,2,2], [2,2,2,3,3], [3,3,3,3], [2,2,3,5] and [2,5,5].

MATHEMATICA

Table[Rest@CoefficientList[Series[1/Times @@ ((1-x^#)& /@ (First /@ FactorInteger[n])), {x, 0, n}], x], {n, 2, 24}]

CROSSREFS

Cf. A066882.

Sequence in context: A096563 A216512 A078359 * A263717 A230279 A085859

Adjacent sequences:  A107326 A107327 A107328 * A107330 A107331 A107332

KEYWORD

easy,nonn,tabl

AUTHOR

Wouter Meeussen, May 22 2005

STATUS

approved

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Last modified September 25 03:24 EDT 2020. Contains 337333 sequences. (Running on oeis4.)