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Search: id:A090477
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| A090477 |
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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. |
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1
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| 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
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OFFSET
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1,23
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EXAMPLE
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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.
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CROSSREFS
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Cf. A000040, A000041.
Sequence in context: A030353 A089617 A128521 this_sequence A087479 A039978 A099918
Adjacent sequences: A090474 A090475 A090476 this_sequence A090478 A090479 A090480
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KEYWORD
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nonn,tabl
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 01 2004
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