cp's OEIS Frontend

A050495 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).

%I A050495 #15 Oct 02 2019 01:58:32
%S A050495 72,144,216,216,288,432,432,576,648,648,792,864,864,1080,1152,1224,
%T A050495 1296,1296,1368,1446,1512,1584,1656,1728,1728,1944,1944,2088,2160,
%U A050495 2232,2304,2376,2376,2448,2592,2592,2664,2736,2892,2952,3024,3096,3168
%N A050495 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 A050495 A number can occur multiple times, corresponding to the number of these arithmetic progressions that it starts. - _Robert Israel_, Nov 29 2016
%H A050495 Robert Israel, <a href="/A050495/b050495.txt">Table of n, a(n) for n = 1..2704</a>
%e A050495 phi(72) = phi(78) = phi(84) = phi(90) = 24, so 72 is a member of the sequence.
%p A050495 N:= 5000: # to get all terms <= N
%p A050495 AP4:= proc(S) local res, n, i1,i4;
%p A050495    n:= nops(S); res:= NULL;
%p A050495    for i1 from 1 to n-3 do
%p A050495      for i4 from i1+3 to n do
%p A050495        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 A050495        fi
%p A050495    od od;
%p A050495    [res]
%p A050495 end proc:
%p A050495 Res:= NULL:
%p A050495 for m from 1 to N-1 do
%p A050495   Res:= Res, op(select(`<=`,AP4(numtheory:-invphi(m)),N));
%p A050495 od:
%p A050495 sort([Res]); # _Robert Israel_, Nov 29 2016
%Y A050495 Cf. A000010, A050496, A050497.
%K A050495 nonn
%O A050495 1,1
%A A050495 _Jud McCranie_, Dec 27 1999