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Search: id:A091050
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| A091050 |
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Number of divisors of n that are perfect powers. |
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+0
3
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| 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 2, 2, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 5, 1, 2, 2, 4, 1, 1
(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)=1 iff n is square-free: a(A005117(n))=1, a(A013929(n))>1;
a(p^k)=k for p prime, k>0: a(A000961(n))=A025474(n);
not the same as A005361: a(72)=5 <> A005361(72)=6.
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LINKS
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Eric Weisstein's World of Mathematics, Perfect Power
Eric Weisstein's World of Mathematics, Divisor Function
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FORMULA
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a(n) = A073093(n)-A001221(n) = A001222(n)-A001221(n)+1. - David W. Wilson (davidwwilson(AT)comcast.net), Aug 28 2007
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EXAMPLE
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Divisors of n=108: {1,2,3,4,6,9,12,18,27,36,54,108}, a(108) =
#{1^2, 2^2, 3^2, 3^3, 6^2} = 5.
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CROSSREFS
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Cf. A091051, A001597, A000005.
Sequence in context: A051903 A157754 A072411 this_sequence A005361 A008479 A107345
Adjacent sequences: A091047 A091048 A091049 this_sequence A091051 A091052 A091053
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 15 2003
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