A125735 5-Multiply SENSigma Perfect Number.

23127045480000, 120046268160000, 33326072536680000

Offset

1,1

Comments

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.

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

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

Links

Table of n, a(n) for n=1..3.

Formula

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

Example

Factorizations:
23127045480000 = 2^6*3^4*5^4*7^2*11*17*19*41.
120046268160000 = 2^11*3^3*5^4*7^3*13*19*41.
33326072536680000 = 2^6*3^4*5^4*7^2*11^2*17*19*41*131.

Crossrefs

Sequence in context: A246110 A015438 A082249 * A317777 A017544 A221560

Adjacent sequences: A125732 A125733 A125734 * A125736 A125737 A125738

Keyword

nonn,bref

Author

Yasutoshi Kohmoto, Jan 01 2007

Extensions

New name and overall edit by Michel Marcus, Apr 27 2013

Status

approved