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Search: id:A068976
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| A068976 |
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Sum( d divides n,d/core(d)) where core(x) is the smallest number such that x*core(x) is a square. |
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+0
4
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| 1, 2, 2, 6, 2, 4, 2, 10, 11, 4, 2, 12, 2, 4, 4, 26, 2, 22, 2, 12, 4, 4, 2, 20, 27, 4, 20, 12, 2, 8, 2, 42, 4, 4, 4, 66, 2, 4, 4, 20, 2, 8, 2, 12, 22, 4, 2, 52, 51, 54, 4, 12, 2, 40, 4, 20, 4, 4, 2, 24, 2, 4, 22, 106, 4, 8, 2, 12, 4, 8, 2, 110, 2, 4, 54, 12, 4, 8, 2, 52, 101, 4, 2, 24, 4, 4, 4
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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More generally, a(n,m) = Sum_{d divides n} gcd(d,n/d)^m is multiplicative with a(p^e,m) = (p^(m*e/2)*(p^m+1)-2)/(p^m-1) if e is even else 2*(p^(m*(e+1)/2)-1)/(p^m-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 30 2003
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FORMULA
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a(n) = Sum_{d divides n} gcd(d, n/d)^2. Multiplicative with a(p^e) = (p^(e+2)+p^e-2)/(p^2-1) if e is even else 2*(p^(e+1)-1)/(p^2-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 30 2003
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CROSSREFS
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Cf. A055155.
Sequence in context: A162299 A110141 A129750 this_sequence A124859 A021446 A062401
Adjacent sequences: A068973 A068974 A068975 this_sequence A068977 A068978 A068979
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KEYWORD
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easy,nonn,mult
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 06 2002
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