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A286779
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Multiplicative with a(p^e) = 2e^2 + 2.
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3
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1, 4, 4, 10, 4, 16, 4, 20, 10, 16, 4, 40, 4, 16, 16, 34, 4, 40, 4, 40, 16, 16, 4, 80, 10, 16, 20, 40, 4, 64, 4, 52, 16, 16, 16, 100, 4, 16, 16, 80, 4, 64, 4, 40, 40, 16, 4, 136, 10, 40, 16, 40, 4, 80, 16, 80, 16, 16, 4, 160, 4, 16, 40, 74, 16, 64, 4, 40, 16
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OFFSET
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1,2
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COMMENTS
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If n is odd, then a(n) is the number of non-isomorphic generalized quaternion rings over Z_n.
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LINKS
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FORMULA
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MAPLE
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a:= n-> mul(2*i[2]^2+2, i=ifactors(n)[2]):
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MATHEMATICA
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fa[n_] := fa[n] = FactorInteger[n]; phi[1] = 1; phi[p_, s_] := 2s^2 + 2;
phi[n_] := Product[phi[fa[n][[i, 1]], fa[n][[i, 2]]], {i, Length[fa[n]]}];
Table[phi[n], {n, 1, 44}]
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PROG
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CROSSREFS
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KEYWORD
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nonn,mult,easy
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AUTHOR
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STATUS
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approved
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