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A125141 a(1) = 2; for n>1, a(n)=SENSigma(a(n-1)), where SENSigma(m) = (-1)^((Sum_i r_i)+Omega(m))*Sum_{d|m} (-1)^((Sum_j Max(r_j))+Omega(d))*d = Product_i (Sum_{1<=s_i<=r_i} p_i^s_i)+(-1)^(r_i+1) if m=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 m. 3
2, 3, 4, 5, 6, 12, 20, 30, 72, 165, 288, 693, 1056, 3024, 9280, 22500, 42845, 60480, 240000, 794580, 1814400, 7040040, 26352000, 98654400, 321552000, 1260230400, 5311834416, 17570520000, 75087810000, 325180275840, 1526817600000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

By "Max(r_j)" is meant 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..31.

MAPLE

SENSigma := 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: A125141 := proc(nmax) local a ; a := [2] ; while nops(a)< nmax do a := [op(a), SENSigma(op(-1, a))] ; od ; RETURN(a) ; end: A125141(40) ; # R. J. Mathar, May 18 2007

CROSSREFS

Cf. A126851, A126852, A125142.

Sequence in context: A273733 A218345 A059460 * A282505 A165304 A266642

Adjacent sequences:  A125138 A125139 A125140 * A125142 A125143 A125144

KEYWORD

nonn

AUTHOR

Yasutoshi Kohmoto, Jan 12 2007

EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 14 2007

More terms from R. J. Mathar, May 18 2007

STATUS

approved

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Last modified November 13 11:34 EST 2018. Contains 317133 sequences. (Running on oeis4.)