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A125141
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a(1) = 2; for n>1, a(n)=SENSigma(a(n-1)), where SENSigma(m) = (-1)^((Sum_i r_i)+Omega(m))*Sum_{d|m} (-1)^((Sum_j Max(r_j))+Omega(d))*d = Product_i (Sum_{1<=s_i<=r_i} p_i^s_i)+(-1)^(r_i+1) if m=Product_i p_i^r_i, d=Product_j p_j^r_j, p_j^max(r_j) is the largest power of p_j dividing m.
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3
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2, 3, 4, 5, 6, 12, 20, 30, 72, 165, 288, 693, 1056, 3024, 9280, 22500, 42845, 60480, 240000, 794580, 1814400, 7040040, 26352000, 98654400, 321552000, 1260230400, 5311834416, 17570520000, 75087810000, 325180275840, 1526817600000
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OFFSET
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1,1
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COMMENTS
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By "Max(r_j)" is meant the following: if d|m, d=p^e*q^f, m=p^x*q^y*r^z then Max(e)=x, Max(f)=y.
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LINKS
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MAPLE
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SENSigma := proc(n) local ifs, i, a, r, p ; ifs := ifactors(n)[2] ; a := 1 ; for i from 1 to nops(ifs) do r := op(2, op(i, ifs)) ; p := op(1, op(i, ifs)) ; a := a*(p*(1-p^r)/(1-p)-(-1)^r) ; od ; RETURN(a) ; end: A125141 := proc(nmax) local a ; a := [2] ; while nops(a)< nmax do a := [op(a), SENSigma(op(-1, a))] ; od ; RETURN(a) ; end: A125141(40) ; # R. J. Mathar, May 18 2007
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MATHEMATICA
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SENSigma[n_] := Module[{Ifs, i, a, r, p }, Ifs = FactorInteger[n]; a = 1; For[i = 1, i <= Length[Ifs], i++, r = Ifs[[i, 2]]; p = Ifs[[i, 1]]; a = a(p(1 - p^r)/(1 - p) - (-1)^r)]; Return[a]];
A125141[nmax_] := Module[{a}, a = {2}; While[Length[a] < nmax, a = Append[a, SENSigma[a[[-1]]]]]; Return[a]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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