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Search: id:A065704
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| A065704 |
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Number or squares or twice squares dividing n. |
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+0
2
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| 1, 2, 1, 3, 1, 2, 1, 4, 2, 2, 1, 3, 1, 2, 1, 5, 1, 4, 1, 3, 1, 2, 1, 4, 2, 2, 2, 3, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 4, 1, 2, 1, 3, 2, 2, 1, 5, 2, 4, 1, 3, 1, 4, 1, 4, 1, 2, 1, 3, 1, 2, 2, 7, 1, 2, 1, 3, 1, 2, 1, 8, 1, 2, 2, 3, 1, 2, 1, 5, 3, 2, 1, 3, 1, 2, 1, 4, 1, 4, 1, 3, 1, 2, 1, 6, 1, 4, 2, 6, 1, 2, 1, 4, 1
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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1/2*Sum_{ d divides n } (1-(-1)^sigma(d)). Multiplicative with a(2^e) = e+1 and a(p^e) = floor(e/2)+1 for an odd prime p.
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EXAMPLE
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divisors(36) = {1, 2, 3, 4, 6, 9, 12, 18, 36}, thus a(36) = #{1, 2, 4, 9, 18, 36}=6. a(36) = 1/2*(tau(36)-((-1)^sigma(1)+(-1)^sigma(2)+(-1)^sigma(3)+(-1)^sigma(4)+(-1)^sigma(6)+(-1)^sigma(9)+(-1)^sigma(12)+(-1)^sigma(18)+(-1)^sigma(36))) = 1/2*(9-(-3)) = 6. a(36) = a(2^2*3^2) = a(2^2)*a(3^2) = (2+1)*(1+1) = 6.
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CROSSREFS
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Cf. A000203, A028982, A046951.
Sequence in context: A156249 A164677 A001511 this_sequence A026100 A059127 A105609
Adjacent sequences: A065701 A065702 A065703 this_sequence A065705 A065706 A065707
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KEYWORD
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mult,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 04 2001
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Sep 09 2002
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