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Search: id:A158378
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| 0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n) for n >= 2 equals GCD of minimal and maximal exponents in prime factorization of n. For n >= 2 holds: a(n)*A157754(n) = A051904(n)*A051903(n). a(n) for n >= 2 it deviates from A052409(n), first different term is a(10800)=a(2^4*3^3*5^2), a(10800)=GCD(2,4)=2, A052409(10800)= GCD(2,3,4)=1.
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FORMULA
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a(1) = 0, a(p) = 1, a(pq) = 1, a(pq...z) = 1, a(p^k) = k, for p = primes (A000040), pq = product of two distinct primes (A006881), pq...z = product of k (k > 2) distinct primes p, q, ..., z (A120944), p^k = prime powers (A000961(n) for n > 1), k = natural numbers (A000027).
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EXAMPLE
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For n=12=2^2*3^1 the a(12)=GCD(2,1)=1.
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CROSSREFS
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Cf.: A157754, A051904, A051903, A052409.
Sequence in context: A037861 A145037 A158052 this_sequence A052409 A051904 A070012
Adjacent sequences: A158375 A158376 A158377 this_sequence A158379 A158380 A158381
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KEYWORD
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nonn
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AUTHOR
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Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 17 2009
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