

A208507


Reordering of A070776 such that the cyclotomic polynomial Phi(A070776, m) is in sorted order for any integer m >= 2.


1



1, 2, 6, 4, 3, 10, 12, 8, 5, 14, 18, 9, 7, 20, 24, 16, 22, 11, 26, 28, 36, 13, 34, 40, 48, 32, 17, 38, 54, 27, 19, 44, 50, 25, 46, 23, 52, 56, 72, 58, 29, 62, 31, 68, 80, 96, 64, 74, 76, 108, 37, 82, 88, 100, 41, 86, 98, 49, 43, 92, 94, 47, 104, 112, 144
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OFFSET

1,2


COMMENTS

When p is an odd prime number and i >= 1, j >= 1, the cyclotomic polynomial
Phi(2^i*p^j, k)
= Phi(2p,k^(2^(i1)*p^(j1)))
= Phi(p, (k^(2^(i1)*p^(j1))))
= (111.....1) (p ones) base (k^(2^(i1)*p^(j1)))
Phi(p^j, k)
= Phi(p, k^(p^(j1)))
= (111.....1) (p ones) base k^(p^(j1)).
For odd prime p >= 3, the above numbers can be called "Very Generic Repdigit Numbers".
This sequence is a subsequence of A206225.
The Mathematica program is rewritten to be able to generate this sequence to an arbitrary EulerPhi boundary.


LINKS



EXAMPLE

The first 20 elements of A206225 are 1, 2, 6, 4, 3, 10, 12, 8, 5, 14, 18, 9, 7, 15, 20, 24, 16, 30, 22, 11.
Among these, 15 = 3 * 5 and 30 = 2 * 3 * 5 cannot be written in the form 2^i*p^j and are thus rejected. So the first 18 terms of this sequence are 1, 2, 6, 4, 3, 10, 12, 8, 5, 14, 18, 9, 7, 20, 24, 16, 22, 11.


MATHEMATICA

eb = 48; phiinv[n_, pl_] := Module[{i, p, e, pe, val}, If[pl == {}, Return[If[n == 1, {1}, {}]]]; val = {}; p = Last[pl]; For[e = 0; pe = 1, e == 0  Mod[n, (p  1) pe/p] == 0, e++; pe *= p, val = Join[val, pe*phiinv[If[e == 0, n, n*p/pe/(p  1)], Drop[pl, 1]]]]; Sort[val]]; phiinv[n_] := phiinv[n, Select[1 + Divisors[n], PrimeQ]]; elim = Max[Table[Max[phiinv[n]], {n, 2, eb, 2}]]; t = Select[Range[elim], (a = FactorInteger[#]; b = Length[a]; ((b == 1)  ((b == 2) && (a[[1]][[1]] == 2))) && (EulerPhi[#] <= eb)) &]; SortBy[t, Cyclotomic[#, 2] &]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



