|
Search: id:A125142
|
|
|
| A125142 |
|
a(n) = smallest k such that SEPSigma^{k}(n)=1, or -1 if no such k exists. Here SEPSigma(m) = (-1)^(Sum_i r_i)*Sum_{d|m} (-1)^(Sum_j Max(r_j))*d =Product_i (Sum_{1<=s_i<=r_i} p_i^s_i)+(-1)^r_i where 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. |
|
+0
2
|
|
| 0, 1, 2, 4, 5, 2, 3, 6, 6, 5, 6, 4, 5, 3, 7, 9, 10, 6, 7, 7, 5, 6, 7, 6, 9, 5, 8, 6, 7, 7, 8, 11, 8, 10, 7, -1
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
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.
For n=36, no k exists which matches the definition since the iteration reaches a cycle that toggles between 168 and 156 ad infinitum: 36->91->72->169->183->120->104->156->168->156-> etc. In the same fashion, no solutions exist for n=37,40,41,45,49,52,53,.. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 07 2007
|
|
EXAMPLE
|
SEPSigma^{5}(5)=1, so a(5)=5: 5 -> 4 -> 7 -> 6 -> 2 -> 1
|
|
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: A125142 := proc(n) local a, nsep; nsep := n ; a :=0 ; while nsep <> 1 do a := a+1 ; nsep := A125140(nsep) ; od ; RETURN(a) ; end: for n from 1 to 80 do printf("%d, ", A125142(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 07 2007
|
|
CROSSREFS
|
Cf. A126851-A126852, A125140, A125141.
Sequence in context: A075884 A030750 A059215 this_sequence A096352 A071286 A021807
Adjacent sequences: A125139 A125140 A125141 this_sequence A125143 A125144 A125145
|
|
KEYWORD
|
sign,more
|
|
AUTHOR
|
Yasutoshi Kohmoto zbi74583(AT)boat.zero.ad.jp, Jan 12 2007, Jan 29 2007
|
|
EXTENSIONS
|
Edited by njas at the suggestions of Andrew Plewe and R. J. Mathar, May 14 2007, Jun 10 2007
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 07 2007
|
|
|
Search completed in 0.002 seconds
|
