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Search: id:A091051
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| A091051 |
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Sum of divisors of n that are perfect powers. |
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+0
2
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| 1, 1, 1, 5, 1, 1, 1, 13, 10, 1, 1, 5, 1, 1, 1, 29, 1, 10, 1, 5, 1, 1, 1, 13, 26, 1, 37, 5, 1, 1, 1, 61, 1, 1, 1, 50, 1, 1, 1, 13, 1, 1, 1, 5, 10, 1, 1, 29, 50, 26, 1, 5, 1, 37, 1, 13, 1, 1, 1, 5, 1, 1, 10, 125, 1, 1, 1, 5, 1, 1, 1, 58, 1, 1, 26, 5, 1, 1, 1, 29, 118, 1, 1, 5, 1, 1, 1, 13, 1, 10
(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)=1+(p^2)*(p^(k-1)-1)/(p-1) for p prime, k>0: a(A000961(n))=A086455(n)-A025473(n).
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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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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 = 1+4+9+27+36 = 77.
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CROSSREFS
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Cf. A091050, A001597, A000005.
Sequence in context: A066504 A140210 A010130 this_sequence A130511 A011396 A036791
Adjacent sequences: A091048 A091049 A091050 this_sequence A091052 A091053 A091054
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Dec 15 2003
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