

A208507


Reorder of A070776 such that 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, 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))
As of odd prime p >= 3, the above numbers can be called "Very Generic Repdigit Numbers".
This sequence is a subset of A206225.
The mathematica program is rewritten to be able to generate this sequence to arbitrary EulerPhi boundary.


LINKS

Table of n, a(n) for n=1..65.


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 which 15 = 3 * 5 and 30 = 2 * 3 * 5 cannot be written in the form of 2^i*p^j and thus rejected. So the first 18 elements 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

Cf. A070776, A206225.
Sequence in context: A286451 A102510 A206225 * A216153 A100115 A029670
Adjacent sequences: A208504 A208505 A208506 * A208508 A208509 A208510


KEYWORD

nonn,easy


AUTHOR

Lei Zhou, Feb 27 2012


STATUS

approved



