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 A126851 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. 3
 1, 2, 2, 7, 6, 6, 7, 15, 11, 18, 10, 14, 14, 18, 12, 31, 18, 33, 18, 42 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA 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) EXAMPLE SPM4Sigma(240) = (1+2+4+8+16)*(-1+3)*(1+5). CROSSREFS Cf. A126852. Sequence in context: A006748 A193548 A131049 * A142070 A152825 A261710 Adjacent sequences:  A126848 A126849 A126850 * A126852 A126853 A126854 KEYWORD nonn,uned AUTHOR Yasutoshi Kohmoto, Feb 24 2007 STATUS approved

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Last modified July 3 10:20 EDT 2020. Contains 335417 sequences. (Running on oeis4.)