A125735 - OEIS

%I #11 Apr 19 2016 01:16:09

%S 23127045480000,120046268160000,33326072536680000

%N 5-Multiply SENSigma Perfect Number.

%C SENSigma(n)=5*n where SENSigma(m) = (-1)^((Sum_i r_i)+Omega(m))*Sum_{d|m} (-1)^((Sum_j r_j)+Omega(d))*d =Product_i (Sum_{1<=s_i<=r_i} p_i^s_i)+(-1)^(r_i+1) where m=Product_i p_i^r_i, d=Product_j p_j^r_j.

%C SEN is for Signed by Exponents of prime factors and Number of prime factors.

%C For instance, SENSigma(240) = (-1+2+4+8+16)*(1+3)*(1+5) = 696.

%F SENSigma(n)=Product_i (p_i^(r_i+1)-p_i)/(p_i-1)+(-1)^(r_i+1)

%e Factorizations:

%e 23127045480000 = 2^6*3^4*5^4*7^2*11*17*19*41.

%e 120046268160000 = 2^11*3^3*5^4*7^3*13*19*41.

%e 33326072536680000 = 2^6*3^4*5^4*7^2*11^2*17*19*41*131.

%K nonn,bref

%O 1,1

%A _Yasutoshi Kohmoto_, Jan 01 2007

%E New name and overall edit by _Michel Marcus_, Apr 27 2013