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A348304
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a(n) = Sum_{d|n} d'', where d'' is the second arithmetic derivative of d (A068346).
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1
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0, 0, 0, 4, 0, 1, 0, 20, 5, 1, 0, 37, 0, 6, 12, 100, 0, 16, 0, 49, 7, 1, 0, 101, 7, 8, 32, 90, 0, 15, 0, 276, 9, 1, 16, 144, 0, 10, 32, 137, 0, 15, 0, 117, 33, 10, 0, 421, 9, 47, 24, 104, 0, 151, 32, 202, 13, 1, 0, 191, 0, 14, 32, 916, 21, 12, 0, 161, 15, 24, 0, 428, 0, 16, 35
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OFFSET
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1,4
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COMMENTS
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Sum of the 2nd arithmetic derivatives of the divisors of n.
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LINKS
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FORMULA
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a(p) = 0 for primes p, since we have 1'' + p'' = 0' + 1' = 0 + 0 = 0.
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EXAMPLE
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a(8) = 20; a(8) = 1'' + 2'' + 4'' + 8'' = 0 + 0 + 4 + 16 = 20.
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PROG
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(PARI) ad(n) = vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
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CROSSREFS
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Inverse Möbius transform of A068346 (2nd arithmetic derivative).
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KEYWORD
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AUTHOR
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STATUS
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approved
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