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A098235 Number of ways to write n as a sum of two ordered positive squarefree numbers. 18
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
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(n) = Sum_{k=1..n-1} (mu(k)*mu(n-k))^2. - Benoit Cloitre, Sep 24 2006
a(n) = Sum_{k=1..n-1} ( A008966(k)*A008966(n-k) ). - 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) a(n) = sum(k=1, n-1, (moebius(k)*moebius(n-k))^2) \\ Indranil Ghosh, Mar 10 2017
(PARI) a(n)=my(s); forsquarefree(k=1, n-1, s+=issquarefree(n-k)); s \\ Charles R Greathouse IV, Jan 08 2018
CROSSREFS
Sequence in context: A255395 A175266 A320053 * A342847 A345873 A114868
KEYWORD
nonn
AUTHOR
Ralf Stephan, Aug 31 2004
STATUS
approved

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Last modified July 22 10:40 EDT 2024. Contains 374490 sequences. (Running on oeis4.)