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Search: id:A126851
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| A126851 |
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SPM4Sigma(n) = (-1)^(1/2*((Sum_i p_i)-Omega(m'))*Sum_{d|n} (-1)^(1/2*((Sum_j p_j)-Omega(d'))*d =(2^(r+1)-1)*Product_i (Sum_{1<=s_i<=r_i} p_i^s_i)+(-1)^(1/2*(p_i-1)) where n=2^r*m', GCD(2,m')=1, m'=Product_i p_i^r_i, d=2^k*d', GCD(2,d')=1, d'=Product_j p_j^r_j SPM4 for Signed by Prime factors Mod 4. |
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+0
4
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| 1, 2, 2, 7, 6, 6, 7, 15, 11, 18, 10, 14, 14, 18, 12, 31, 18, 33, 18, 42
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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SPM4Sigma(n)=(2^r-1)*Product_i (p_i^(r_i+1)-p_i)/(p_i-1)+(-1)^(1/2*(p_i-1)) =(2^r-1)*Product_{i=1 mod 4} ((p_i^(r_i+1)-p_i)/(p_i-1)+1)*Product_{i=3 mod 4} ((p_i^(r_i+1)-p_i)/(p_i-1)-1)
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EXAMPLE
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SPM4Sigma(240)=(1+2+4+8+16)*(-1+3)*(1+5)
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CROSSREFS
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Cf. A126852.
Sequence in context: A058625 A006748 A131049 this_sequence A142070 A152825 A064288
Adjacent sequences: A126848 A126849 A126850 this_sequence A126852 A126853 A126854
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KEYWORD
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nonn,mult,uned
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AUTHOR
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Yasutoshi Kohmoto zbi74583(AT)boat.zero.ad.jp, Feb 24 2007
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