A050520 Values of phi in arithmetic progression of at least 6 terms having the same value of phi in A050518.

155520, 311040, 466560, 622080, 777600, 933120, 933120, 1244160, 1399680, 1555200, 1555200, 1866240, 1866240, 1866240, 2332800, 2488320, 2488320, 2799360, 2799360, 3110400, 2799360, 3110400, 3421440, 3732480, 3888000

Offset: 1

Author

Jud McCranie, Dec 28 1999

Keywords

• nonn

Comments

The values of phi for terms between 13413600 and 10^9 (see comment on A050518) are 3732480, 3888000, 3732480, 4199040, 3732480, 4354560, 4665600, 4665600, 4976640, 4665600, 14999040, 19595520, 29998080, 44130240, 39191040, 44997120, 58786560, 59996160, 88260480, 78382080, 132390720, 134648640, 145313280, 176520960, 220651200, 237948480, 264781440. - Mauro Fiorentini, Apr 17 2015

Links

• Robert Israel, Table of n, a(n) for n = 1..114
• Tanya Khovanova, Non Recursions

Crossrefs

Cf. A000010, A050495, A050496, A050497, A050515-A050520.

Programs

Maple

N:= 10^7: # to get all terms <= N in A050518
with(numtheory):
Res:= NULL:
phis:= {seq(phi(i), i=2..N)}:
for m in phis do
   S:= convert(invphi(m), set);
   if nops(S) < 6 then next fi;
   for d from 0 to 4 do
     Sd[d]:= select(t-> (t mod 5 = d), S, d);
     nd:= nops(Sd[d]);
     for i0 from 1 to nd-1 do
       s0:= Sd[d][i0];
       if s0 > N then break fi;
       for i5 from i0+1 to nd do
         s5:= Sd[d][i5];
         incr:= (s5 - s0)/5;
         if {s0+incr, s0+2*incr, s0+3*incr, s0+4*incr} subset S then
           Res:= Res, [s0, m];
         fi
       od
     od;
   od;
od:
map2(op,2,sort([Res], (s, t)->s[1]Robert Israel, May 10 2015