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

1,1

Comments

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

Links

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

Example

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

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

Crossrefs

Cf. A000010, A050496, A050497.

Sequence in context: A369333 A369334 A060661 * A137883 A173728 A173547

Adjacent sequences: A050492 A050493 A050494 * A050496 A050497 A050498

Keyword

nonn

Author

Jud McCranie, Dec 27 1999

Status

approved