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A060940 Triangle in which n-th row gives the phi(n) terms appearing as initial primes in arithmetic progressions with difference n, with initial term equal to the smallest positive residue coprimes to n.

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%I A060940 #23 Feb 16 2025 08:32:44
%S A060940 2,3,7,5,5,7,11,7,13,19,7,11,29,23,17,11,19,13,17,11,13,23,19,11,13,
%T A060940 23,43,17,11,13,17,19,23,13,47,37,71,17,29,19,31,43,13,17,19,23,53,41,
%U A060940 29,17,31,19,59,47,61,23,37,103,29,17,19,23,53,41,31,17,19,37,23,41,43,29
%N A060940 Triangle in which n-th row gives the phi(n) terms appearing as initial primes in arithmetic progressions with difference n, with initial term equal to the smallest positive residue coprimes to n.
%H A060940 Seiichi Manyama, <a href="/A060940/b060940.txt">Rows n = 1..200, flattened</a>
%H A060940 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/DirichletsTheorem.html">Dirichlet's theorem</a>
%H A060940 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet%27s_theorem_on_arithmetic_progressions">Dirichlet's theorem on arithmetic progressions</a>
%e A060940 For differences 1, 2, 3, 4, 5, 6, 7, .. the initial primes are 2; 3; 7, 5; 5, 7; 11, 7, 13, 19; 7, 11; 29, 23, 17, 11, 19, 13; ... etc. Suitable initial values (coprimes to difference) are in A038566. Position of end(start) of rows is given by values of A002088.
%e A060940 From _Seiichi Manyama_, Apr 02 2018: (Start)
%e A060940    n | phi(n)|
%e A060940   ---+-------+------------------------
%e A060940    1 |   1   |  2;
%e A060940    2 |   1   |  3;
%e A060940    3 |   2   |  7,  5;
%e A060940    4 |   2   |  5,  7;
%e A060940    5 |   4   | 11,  7, 13, 19;
%e A060940    6 |   2   |  7, 11;
%e A060940    7 |   6   | 29, 23, 17, 11, 19, 13;
%e A060940    8 |   4   | 17, 11, 13, 23;
%e A060940    9 |   6   | 19, 11, 13, 23, 43, 17;
%e A060940   10 |   4   | 11, 13, 17, 19;         (End)
%Y A060940 Cf. A000010 (phi), A002088, A038566, A034693, A034694, A002144, A007519, A088732, etc..
%K A060940 nonn,tabf
%O A060940 1,1
%A A060940 _Labos Elemer_, May 07 2001