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Numbers that are the first term of at least one arithmetic progression with 4 or more terms all having the same value of Euler's totient function phi(x).
9

%I #15 Oct 02 2019 01:58:32

%S 72,144,216,216,288,432,432,576,648,648,792,864,864,1080,1152,1224,

%T 1296,1296,1368,1446,1512,1584,1656,1728,1728,1944,1944,2088,2160,

%U 2232,2304,2376,2376,2448,2592,2592,2664,2736,2892,2952,3024,3096,3168

%N Numbers that are the first term of at least one arithmetic progression with 4 or more terms all having the same value of Euler's totient function phi(x).

%C A number can occur multiple times, corresponding to the number of these arithmetic progressions that it starts. - _Robert Israel_, Nov 29 2016

%H Robert Israel, <a href="/A050495/b050495.txt">Table of n, a(n) for n = 1..2704</a>

%e phi(72) = phi(78) = phi(84) = phi(90) = 24, so 72 is a member of the sequence.

%p N:= 5000: # to get all terms <= N

%p AP4:= proc(S) local res, n, i1,i4;

%p n:= nops(S); res:= NULL;

%p for i1 from 1 to n-3 do

%p for i4 from i1+3 to n do

%p if (S[i1] - S[i4]) mod 3 = 0 and has(S, (2*S[i1]+S[i4])/3) and has(S, (S[i1]+2*S[i4])/3) then res:= res, S[i1]

%p fi

%p od od;

%p [res]

%p end proc:

%p Res:= NULL:

%p for m from 1 to N-1 do

%p Res:= Res, op(select(`<=`,AP4(numtheory:-invphi(m)),N));

%p od:

%p sort([Res]); # _Robert Israel_, Nov 29 2016

%Y Cf. A000010, A050496, A050497.

%K nonn

%O 1,1

%A _Jud McCranie_, Dec 27 1999