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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). 9
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 (list; graph; refs; listen; history; text; internal format)
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: A250772 A157336 A060661 * A137883 A173728 A173547

Adjacent sequences:  A050492 A050493 A050494 * A050496 A050497 A050498

KEYWORD

nonn,changed

AUTHOR

Jud McCranie, Dec 27 1999

STATUS

approved

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)