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.

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

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

Mathematica

SENSigma[n_] := Module[{Ifs, i, a, r, p }, Ifs = FactorInteger[n]; a = 1; For[i = 1, i <= Length[Ifs], i++, r = Ifs[[i, 2]]; p = Ifs[[i, 1]]; a = a(p(1 - p^r)/(1 - p) - (-1)^r)]; Return[a]];
A125141[nmax_] := Module[{a}, a = {2}; While[Length[a] < nmax, a = Append[a, SENSigma[a[[-1]]]]]; Return[a]];
A125141[40] (* Jean-François Alcover, Oct 26 2023, after R. J. Mathar *)

Crossrefs

Cf. A126851, A126852, A125142.

Sequence in context: A273733 A218345 A059460 * A350211 A282505 A165304

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