cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A320046 Largest k such that (Z/kZ)* is isomorphic to (Z/nZ)*.

Original entry on oeis.org

2, 2, 6, 6, 10, 6, 18, 12, 18, 10, 22, 12, 26, 18, 30, 30, 34, 18, 54, 30, 42, 22, 46, 24, 50, 26, 54, 42, 58, 30, 62, 32, 66, 34, 90, 42, 74, 54, 90, 60, 82, 42, 98, 66, 90, 46, 94, 60, 98, 50, 102, 90, 106, 54, 150, 84, 114, 58, 118, 60, 122, 62, 126, 102, 130, 66, 134, 102, 138, 90
Offset: 1

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Author

Jianing Song, Oct 04 2018

Keywords

Comments

All terms are even because (Z/kZ)* is isomorphic to (Z/(2k)Z)* for odd k. Most terms are congruent to 2 modulo 4. Among the first 10000 terms there are 8980 ones congruent to 2 modulo 4.

Examples

			The solutions to (Z/kZ)* = C_6 are k = 7, 9, 14 and 18, so a(7) = a(9) = a(14) = a(18) = 18.
The solutions to (Z/kZ)* = C_2 X C_20 are k = 55, 75, 100, 110 and 150, so a(55) = a(75) = a(100) = a(110) = a(150) = 150.
The solutions to (Z/kZ)* = C_2 X C_12 are k = 35, 39, 45, 52, 70, 78 and 90, so a(35) = a(39) = a(45) = a(52) = a(70) = a(78) = a(90) = 90.

Links

Crossrefs

Cf. A028476, A057635, A320045.

Programs

  • PARI
    a(n) = if(abs(n)==1||abs(n)==2, 2, my(i=0, search_max = A057635(eulerphi(n))); for(j=eulerphi(n)+1, search_max, if(znstar(j)[2]==znstar(n)[2], i=j)); i) \\ search_max is the largest k such that phi(k) = phi(n). See A057635 for its program

Formula

n <= a(n) <= A028476(n).
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