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A065608
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Sum of divisors of n minus the number of divisors of n.
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13
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0, 1, 2, 4, 4, 8, 6, 11, 10, 14, 10, 22, 12, 20, 20, 26, 16, 33, 18, 36, 28, 32, 22, 52, 28, 38, 36, 50, 28, 64, 30, 57, 44, 50, 44, 82, 36, 56, 52, 82, 40, 88, 42, 78, 72, 68, 46, 114, 54, 87, 68, 92, 52, 112, 68, 112, 76, 86, 58, 156, 60, 92, 98, 120, 80, 136, 66, 120, 92
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Number of permutations p of {1,2,...,n} such that p(k)-k takes exactly two distinct values. Example: a(4)=4 because we have 4123, 3412, 2143 and 2341. (Max Alekseyev and Emeric Deutsch) - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 22 2006
Number of solutions to the Diophantine equation xy + yz = n, with x,y,x >= 1.
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REFERENCES
| M. Alekseev, E. Deutsch, and J. H. Steelman, Problem 11281, Amer. Math. Monthly, 116, No. 5, 2009, p. 465. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 23 2009]
Andrews, George E., Stacked lattice boxes, Ann. Comb. 3 (1999), 115-130. See L_2(n).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| a(n) = A000203(n)-A000005(n).
G.f.: sum(k>=1, x^(2k)/(1-x^k)^2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2003
G.f.: sum(n>=1, (n-1)*x^n/(1-x^n)). - Joerg Arndt, Jan 30 2011
a(n) = sigma(n)-d(n) = A000203(n)-A000005(n). [From Omar E. Pol (info(AT)polprimos.com), Dec 12 2008]
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MAPLE
| with(numtheory): seq(sigma(n)-tau(n), n=1..70); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 22 2006
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PROG
| (PARI) { for (n = 1, 1000, a=sigma(n) - numdiv(n); write("b065608.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 23 2009]
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CROSSREFS
| Cf. A000203, A000005.
Cf. A134857.
Starting (1, 2, 4, 4, 8, 6,...), = row sums of triangle A077478. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 12 2007
Starting with "1" = row sums of triangle A176919 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 29 2010]
Sequence in context: A005884 A079890 A180444 * A184396 A077764 A110794
Adjacent sequences: A065605 A065606 A065607 * A065609 A065610 A065611
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KEYWORD
| nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Nov 06 2001
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