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A143078
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Triangle read by rows: row n (n >= 2) has length pi(n) (see A000720) and the k-th term gives the exponent of prime(k) in the prime factorization of n.
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1
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1, 0, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,4
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COMMENTS
| Comments from Jacques ALARDET, Jan 11 2012: If we suppress the 0's at the ends of the rows we get A067255. The number of 0's suppressed is A036234(n)-A061395(n)-1.
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FORMULA
| t(n,m,k)=If[PrimeQ[FactorInteger[n][[m]][[1]]] && FactorInteger[n][[m]][[ 1]] == Prime[k], FactorInteger[n][[m]][[2]], 0]; T(n,m)=vector_sum overk of t(n,m,k).
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EXAMPLE
| Triangle begins
{1},
{0, 1},
{2, 0},
{0, 0, 1},
{1, 1, 0}, (the 6th row, and 6 = prime(1)*prime(2))
{0, 0, 0, 1},
{3, 0, 0, 0},
{0, 2, 0, 0},
{1, 0, 1, 0},
...
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MATHEMATICA
| Clear[t, T, n, m, k]; t[n_, m_, k_] := If[PrimeQ[FactorInteger[ n][[m]][[1]]] && FactorInteger[n][[m]][[1]] == Prime[k], FactorInteger[n][[m]][[2]], 0]; T = Table[Apply[Plus, Table[Table[t[n, m, k], {k, 1, PrimePi[n]}], { m, 1, Length[FactorInteger[n]]}]], {n, 1, 10}]; Flatten[%]
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CROSSREFS
| Cf. A000720, A001222, A067255.
Sequence in context: A025438 A030216 A159459 * A106405 A089310 A129753
Adjacent sequences: A143075 A143076 A143077 * A143079 A143080 A143081
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KEYWORD
| nonn,tabf,easy,more
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 14 2008
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EXTENSIONS
| Edited by N. J. A. Sloane, Jan 12 2012
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