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A098235 Number of ways to write n as a sum of two ordered positive squarefree numbers. 8
0, 1, 2, 3, 2, 3, 4, 6, 4, 3, 4, 7, 6, 5, 6, 10, 8, 8, 6, 11, 8, 9, 8, 14, 10, 9, 10, 13, 10, 9, 10, 16, 12, 13, 12, 22, 14, 13, 14, 22, 16, 15, 18, 25, 20, 15, 16, 26, 20, 16, 14, 27, 20, 20, 14, 26, 20, 21, 18, 29, 22, 21, 22, 30, 22, 21, 22, 35, 24, 25, 22, 42, 26, 27, 26, 39 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) ~ n * Prod[p prime, (1-2/p^2) * Prod[p^2|n, (p^2-1)/(p^2-2)]].

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

P. Pollack, Analytic and Combinatorial Number Theory, Course Notes, p. 122, 202. [?Broken link]

P. Pollack, Analytic and Combinatorial Number Theory, Course Notes, p. 122, 202.

FORMULA

a(1)=0 then a(n+1) = Sum_{k=1..n} (mu(k)*mu(n+1-k))^2. - Benoit Cloitre, Sep 24 2006

a(n+1) = Sum_{k=1..n} ( A008966(k)*A008966(n-k+1) ). - Reinhard Zumkeller, Nov 04 2009

G.f.: ( Sum_{k>=1} mu(k)^2*x^k )^2, where mu(k) is the Moebius function (A008683). - Ilya Gutkovskiy, Dec 28 2016

EXAMPLE

a(12)=7 because 12=1+11=2+10=5+7=6+6=7+5=10+2=11+1.

MATHEMATICA

Join[{0}, Table[Sum[(MoebiusMu[k]*MoebiusMu[n - k + 1])^2, {k, 1, n}], {n, 1, 50}]] (* G. C. Greubel, Dec 28 2016 *)

PROG

(PARI) for(n=0, 75, print1(sum(k=1, n, (moebius(k)*moebius(n - k + 1))^2), ", ")) \\ Indranil Ghosh, Mar 10 2017

CROSSREFS

Cf. A005117, A098236.

Cf. A071068.

Sequence in context: A275727 A255395 A175266 * A114868 A249049 A138239

Adjacent sequences:  A098232 A098233 A098234 * A098236 A098237 A098238

KEYWORD

nonn

AUTHOR

Ralf Stephan, Aug 31 2004

STATUS

approved

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Last modified May 23 08:43 EDT 2017. Contains 286909 sequences.