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A125140 SEPSigma(n) = (-1)^(Sum_i r_i)*Sum_{d|n} (-1)^(Sum_j Max(r_j))*d =Product_i (Sum_{1<=s_i<=r_i} p_i^s_i)+(-1)^r_i where n=Product_i p_i^r_i, d=Product_j p_j^r_j, p_j^max(r_j) is the largest power of p_j dividing n. 2
1, 1, 2, 7, 4, 2, 6, 13, 13, 4, 10, 14, 12, 6, 8, 31, 16, 13, 18, 28, 12, 10, 22, 26, 31, 12, 38, 42, 28, 8, 30, 61, 20, 16, 24, 91, 36, 18, 24, 52, 40, 12, 42, 70, 52, 22, 46, 62, 57, 31, 32, 84, 52, 38, 40, 78, 36, 28, 58, 56, 60, 30, 78, 127, 48, 20, 66, 112, 44, 24, 70, 169, 72 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

SEP stands for Signed by Exponents of Prime factors.

By "Max(r_j)" I mean the following: If d|m, d=p^e*q^f, m=p^x*q^y*r^z then Max(e)=x, Max(f)=y.

LINKS

Table of n, a(n) for n=1..73.

FORMULA

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

EXAMPLE

Example : If n=240, d=12 then 2^max(r_j)=2^max(2)=2^4, 3^max(r_j)=3^max(1)=3^1 SEPSigma(240)=(1+2+4+8+16)*(-1+3)*(-1+5)

MAPLE

A125140 := proc(n) local ifs, i, a, r, p ; ifs := ifactors(n)[2] ; a := 1 ; for i from 1 to nops(ifs) do r := op(2, op(i, ifs)) ; p := op(1, op(i, ifs)) ; a := a*(p*(1-p^r)/(1-p)+(-1)^r) ; od ; RETURN(a) ; end: for n from 1 to 80 do printf("%d, ", A125140(n)) ; od ; # R. J. Mathar, Jun 07 2007

CROSSREFS

Sequence in context: A051559 A073239 A134882 * A257345 A110637 A092943

Adjacent sequences:  A125137 A125138 A125139 * A125141 A125142 A125143

KEYWORD

nonn,mult

AUTHOR

Yasutoshi Kohmoto, Jan 12 2007, Jan 29 2007

EXTENSIONS

More terms from R. J. Mathar, Jun 07 2007

STATUS

approved

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Last modified January 22 12:13 EST 2019. Contains 319363 sequences. (Running on oeis4.)