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A125735 5-Multiply SENSigma Perfect Number. 0
23127045480000, 120046268160000, 33326072536680000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 21 20:35 EST 2020. Contains 332111 sequences. (Running on oeis4.)