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A090477 T(n,k) = number of occurrences of k-th prime in the first n partition numbers (with repetitions), 0<=k<n, triangular array read by rows. 0
0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 2, 2, 1, 1, 0, 0, 2, 2, 2, 1, 2, 0, 0, 0, 3, 3, 3, 1, 2, 0, 0, 0, 0, 4, 4, 3, 2, 2, 0, 0, 0, 0, 0, 7, 4, 3, 3, 2, 0, 0, 0, 0, 0, 0, 7, 4, 3, 4, 3, 0, 0, 0, 0, 0, 0, 0, 7, 4, 3, 4, 3, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 4, 4, 3, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,23

LINKS

Table of n, a(n) for n=1..102.

EXAMPLE

Prime factorizations of the first 12 partition numbers:

P(0)=1, P(1)=1, P(2)=2, P(3)=3, P(4)=5, P(5)=7, P(6)=11, P(7)=15=5*3,

P(8)=22=11*2, P(9)=30=5*3*2, P(10)=42=7*3*2 and P(11)=56=7*2^3:

therefore T(11,1)=0+0+1+0+0+0+0+0+1+1+1+3=7 and T(11,2)=0+0+0+1+0+0+0+1+0+1+1+0=4.

CROSSREFS

Cf. A000040, A000041.

Sequence in context: A089617 A274370 A128521 * A293019 A087479 A263343

Adjacent sequences:  A090474 A090475 A090476 * A090478 A090479 A090480

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Feb 01 2004

STATUS

approved

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Last modified October 26 11:29 EDT 2020. Contains 338027 sequences. (Running on oeis4.)