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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 (list; graph; refs; listen; history; text; internal format)
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^(i-1)*p^(j-1)))

  = Phi(p, -(k^(2^(i-1)*p^(j-1))))

  = (111.....1) (p ones) base -(k^(2^(i-1)*p^(j-1)))

Phi(p^j, k)

  = Phi(p, k^(p^(j-1)))

  = (111.....1) (p ones) base k^(p^(j-1))

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

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Last modified October 14 03:00 EDT 2019. Contains 327995 sequences. (Running on oeis4.)