

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 n3 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 N1 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: A345794 A157336 A060661 * A137883 A173728 A173547
Adjacent sequences: A050492 A050493 A050494 * A050496 A050497 A050498


KEYWORD

nonn


AUTHOR

Jud McCranie, Dec 27 1999


STATUS

approved



