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A082786
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Triangle, read by rows, of exponents of primes in canonical prime factorization of n: T(n,k) = greatest number such that prime(k)^T(n,k) divides n, 1 <= k <= n.
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3
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0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1,7
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COMMENTS
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n = Product_{k=1..n} prime(k)^T(n,k);
Sum_{k=1..n} T(n,k)*prime(k) = A001414(n);
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LINKS
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EXAMPLE
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Triangle begins:
0,
1, 0,
0, 1, 0,
2, 0, 0, 0,
0, 0, 1, 0, 0,
1, 1, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0,
3, 0, 0, 0, 0, 0, 0, 0,
...
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MATHEMATICA
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Table[IntegerExponent[n, Prime[k]], {n, 1, 15}, {k, 1, n}] // Flatten (* Amiram Eldar, Dec 14 2018 *)
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PROG
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(PARI) row(n) = vector(n, k, valuation(n, prime(k)));
tabl(nn) = for (n=1, nn, print(row(n))); \\ Michel Marcus, Dec 14 2018
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CROSSREFS
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Cf. A067255 (same as irregular triangle).
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KEYWORD
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AUTHOR
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STATUS
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approved
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