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 A080737 a(1) = a(2) = 0; for n > 2, the least dimension of a lattice possessing a symmetry of order n. 10
 0, 0, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 6, 8, 16, 6, 18, 6, 8, 10, 22, 6, 20, 12, 18, 8, 28, 6, 30, 16, 12, 16, 10, 8, 36, 18, 14, 8, 40, 8, 42, 12, 10, 22, 46, 10, 42, 20, 18, 14, 52, 18, 14, 10, 20, 28, 58, 8, 60, 30, 12, 32, 16, 12, 66, 18, 24, 10, 70, 10, 72, 36, 22, 20, 16, 14 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 J. Bamberg, G. Cairns and D. Kilminster, The crystallographic restriction, permutations and Goldbach's conjecture, Amer. Math. Monthly, 110 (March 2003), 202-209. Savinien Kreczman, Luca Prigioniero, Eric Rowland, and Manon Stipulanti, Magic numbers in periodic sequences, Univ. Liège (Belgium, 2023). See p. 7. FORMULA For n > 2, a(2^r) = 2^(r-1) with r>1, a(p^r) = phi(p^r) with p > 2 prime, r >= 1, where phi is Euler's function A000010; in general if a(Product p_i^e_i) = Sum a(p_i^e_i). MATHEMATICA a[1] = a[2] = 0; a[p_?PrimeQ] := a[p] = p-1; a[n_] := a[n] = If[Length[fi = FactorInteger[n]] == 1, EulerPhi[n], Total[a /@ (fi[[All, 1]]^fi[[All, 2]])]]; Table[a[n], {n, 1, 78}] (* Jean-François Alcover, Jun 20 2012 *) PROG (PARI) for(n=1, 78, k=0; if(n>1, f=factor(n); k=sum(j=1, matsize(f)[1], eulerphi(f[j, 1]^f[j, 2])); if(f[1, 1]==2&&f[1, 2]==1, k--)); print1(k, ", ")) \\ Klaus Brockhaus, Mar 10 2003 (Haskell) a080737 n = a080737_list !! (n-1) a080737_list = 0 : (map f [2..]) where f n | mod n 4 == 2 = a080737 \$ div n 2 | otherwise = a067240 n -- Reinhard Zumkeller, Jun 13 2012, Jun 11 2012 CROSSREFS Cf. A080736, A080738, A080739, A080740, A067240, A000010, A141809. See A152455 for another version. Sequence in context: A011773 A306275 A322321 * A152455 A293484 A000010 Adjacent sequences: A080734 A080735 A080736 * A080738 A080739 A080740 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Mar 08 2003 EXTENSIONS More terms from Klaus Brockhaus, Mar 10 2003 STATUS approved

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Last modified August 7 01:18 EDT 2024. Contains 375002 sequences. (Running on oeis4.)