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Search: id:A125141
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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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+0
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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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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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 (mathar(AT)strw.leidenuniv.nl), May 18 2007
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CROSSREFS
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Cf. A126851, A126852, A125142.
Sequence in context: A108320 A032941 A059460 this_sequence A165304 A115307 A086185
Adjacent sequences: A125138 A125139 A125140 this_sequence A125142 A125143 A125144
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KEYWORD
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nonn
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AUTHOR
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Yasutoshi Kohmoto zbi74583(AT)boat.zero.ad.jp, Jan 12 2007
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, May 14 2007
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2007
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