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).

72, 144, 216, 216, 288, 432, 432, 576, 648, 648, 792, 864, 864, 1080, 1152, 1224, 1296, 1296, 1368, 1446, 1512, 1584, 1656, 1728, 1728, 1944, 1944, 2088, 2160, 2232, 2304, 2376, 2376, 2448, 2592, 2592, 2664, 2736, 2892, 2952, 3024, 3096, 3168

Offset: 1

Author

Jud McCranie, Dec 27 1999

Keywords

• nonn

Comments

A number can occur multiple times, corresponding to the number of these arithmetic progressions that it starts. - Robert Israel, Nov 29 2016

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..2704

Crossrefs

Cf. A000010, A050496, A050497.

Programs

Maple

N:= 5000: # to get all terms <= N
AP4:= proc(S) local res, n, i1,i4;
   n:= nops(S); res:= NULL;
   for i1 from 1 to n-3 do
     for i4 from i1+3 to n do
       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]
       fi
   od od;
   [res]
end proc:
Res:= NULL:
for m from 1 to N-1 do
  Res:= Res, op(select(`<=`,AP4(numtheory:-invphi(m)),N));
od:
sort([Res]); # Robert Israel, Nov 29 2016