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Search: id:A143078
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| A143078 |
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A triangle sequence that gives with rows of primes as factors and columns of n ( row sums are prime divisors A001222). |
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+0
1
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| 0, 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; listen)
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OFFSET
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1,5
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COMMENT
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While the row sums:
{0, 1, 1, 2, 1, 2, 1, 3, 2, 2};
are the prime divisors, the column sum is the frequency
of that primes occur as factors of the counting numbers n:
{9,4,2,1} as 9 twos, 4 threes and 2 fives and one seven in the first ten numbers.
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FORMULA
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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
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0,
{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}
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MATHEMATICA
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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
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Cf. A001222.
Sequence in context: A025438 A030216 A159459 this_sequence A106405 A089310 A129753
Adjacent sequences: A143075 A143076 A143077 this_sequence A143079 A143080 A143081
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KEYWORD
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nonn,uned,tabf
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 14 2008
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