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Search: id:A082786
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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
(list; table; graph; listen)
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OFFSET
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1,7
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COMMENT
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n = Product(prime(k)^T(n,k): 1<=k<=n);
T(n, A055396(n))>0 and T(n,k)=0 for 1<=k<A055396(n);
T(n, A061395(n))>0 and T(n,k)=0 for A061395(n)<k<=n;
Sum(T(n,k): 1<=k<=n) = A001222(n);
Sum(A057427(T(n,k)): 1<=k<=n) = A001221(n);
Sum(T(n,k)*prime(k): 1<=k<=n) = A001414(n);
Sum(A057427(T(n,k))*prime(k): 1<=k<=n) = A008472(n);
Min(T(n,k): 1<=k<=n) = A051904(n);
Max(T(n,k): 1<=k<=n) = A051903(n);
T(n,1)=A007814(n); T(n,2)=A007949(n), n>1.
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LINKS
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Eric Weisstein's World of Mathematics, Prime Factorization.
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CROSSREFS
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Cf. A000040, A049084.
Sequence in context: A083916 A083893 A094428 this_sequence A101638 A070141 A088722
Adjacent sequences: A082783 A082784 A082785 this_sequence A082787 A082788 A082789
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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)lhsystems.com), May 22 2003
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