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A279621
Numbers k such that 1/phi(x) + 1/phi(y) = 1/phi(k), for some x + y = k and phi(k) is the Euler totient function of k.
1
1890, 2100, 2310, 3780, 5250, 7770, 10080, 11310, 11550, 11880, 12180, 13230, 13650, 13860, 14190, 14910, 15750, 17640, 18060, 19950, 20460, 20790, 21630, 22050, 22110, 23100, 24090, 24180, 24570, 25410, 25620, 25830, 26070, 27090, 27510, 27720, 28980, 29040, 29400
OFFSET
1,1
COMMENTS
All terms appear to be multiples of 30.
Terms that are not divisible by 30: 70224, 72072, 96558, 114114, 122892, 156156, 166782, 184338, 191268, ... - Amiram Eldar, Jul 22 2019
LINKS
EXAMPLE
1890 = 817 + 1073 and 1/phi(817) + 1/phi(1073) = 1/756 + 1/1008 = 1/432 = 1/phi(1890).
The first term with more than one solution is 14190:
14190 = 6319 + 7871 and 1/phi(6319) + 1/phi(7871) = 1/6160 + 1/7392 = 1/3360 = 1/phi(14190).
14190 = 6443 + 7747 and 1/phi(6443) + 1/phi(7747) = 1/6048 + 1/7560 = 1/3360 = 1/phi(14190).
MAPLE
with(numtheory): P:= proc(q) local k, n; for n from 1 to q do
for k from 1 to trunc(n/2) do if 1/phi(k)+1/phi(n-k)=1/phi(n)
then print(n); break; fi; od; od; end: P(10^6);
MATHEMATICA
aQ[n_] := Module[{k = 1, r = 1/EulerPhi[n]}, While[2*k <= n && 1/EulerPhi[k] + 1/EulerPhi[n - k] != r, k++]; 2*k <= n]; (* Amiram Eldar, Jul 22 2019 *)
CROSSREFS
Cf. A000010.
Sequence in context: A106764 A157486 A086476 * A168226 A151721 A187743
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Dec 19 2016
STATUS
approved