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A129235
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2*sigma(n)-tau(n), where tau(n) is the number of divisors of n (A000005) and sigma(n) is the sum of divisors of n (A000203).
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10
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1, 4, 6, 11, 10, 20, 14, 26, 23, 32, 22, 50, 26, 44, 44, 57, 34, 72, 38, 78, 60, 68, 46, 112, 59, 80, 76, 106, 58, 136, 62, 120, 92, 104, 92, 173, 74, 116, 108, 172, 82, 184, 86, 162, 150, 140, 94, 238, 111, 180, 140, 190, 106, 232, 140, 232, 156, 176, 118, 324, 122, 188
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums of A129234. [Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2007]
Equals row sums of A130307. [Gary W. Adamson (qntmpkt(AT)yahoo.com), May 20 2007]
Equals row sums of triangle A143315 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 06 2008]
Equals A051731 * (1, 3, 5, 7,...); i.e. the inverse Mobius transform of the odd numbers. Example: a(4) = 11 = (1, 1, 0, 1) * (1, 3, 5, 7) = (1 + 3 + 0 + 7), where (1, 1, 0, 1) = row 4 of A051731. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 17 2008]
Equals row sums of triangle A143594 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 26 2008]
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FORMULA
| G.f.: sum(k>=1, z^k*(k-(k-1)*z^k)/(1-z^k)^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2007
G.f.: sum(n>=1, x^n*(1+x^n)/(1-x^n)^2 ). [Joerg Arndt, May 25 2011]
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EXAMPLE
| a(4)=2*sigma(4)-tau(4)=2*7-3=11.
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MAPLE
| with(numtheory): seq(2*sigma(n)-tau(n), n=1..75); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2007
G:=sum(z^k*(k-(k-1)*z^k)/(1-z^k)^2, k=1..100): Gser:=series(G, z=0, 80): seq(coeff(Gser, z, n), n=1..75); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2007
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CROSSREFS
| Cf. A129234, A129236, A129237.
Cf. A000005, A000203.
Cf. A130307.
A143315 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 06 2008]
A051731 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 17 2008]
A143594 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 26 2008]
Sequence in context: A136838 A109378 A132149 * A012903 A187215 A013018
Adjacent sequences: A129232 A129233 A129234 * A129236 A129237 A129238
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 05 2007
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EXTENSIONS
| Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2007
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