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.

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

Amiram Eldar, Table of n, a(n) for n = 1..1000

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

Adjacent sequences: A279618 A279619 A279620 * A279622 A279623 A279624

Keyword

nonn

Author

Paolo P. Lava, Dec 19 2016

Status

approved