A336384 Numbers of the form k = x*y where phi(k) = 3*(phi(x) + phi(y)).

36, 56, 63, 65, 72, 84, 104, 105, 126, 130, 140, 156, 168, 180, 210

Offset: 1

Author

Jinyuan Wang, Jul 31 2020

Keywords

• nonn
• fini
• full

Comments

There are 35 solutions (x, y) to phi(x*y) = 3*(phi(x) + phi(y)): (4, 14), (4, 18), (5, 13), (5, 21), (5, 26), (5, 28), (5, 36), (5, 42), (6, 6), (6, 14), (7, 9), (7, 18), (8, 13), (8, 21), (9, 7), (9, 14), (10, 13), (10, 21), (12, 13), (13, 5), (13, 8), (13, 10), (13, 12), (14, 4), (14, 6), (14, 9), (18, 4), (18, 7), (21, 5), (21, 8), (21, 10), (26, 5), (28, 5), (36, 5), (42, 5).

Links

• GUO Rui, ZHAO Xiqing, ZHANG Lixia and XU Hongxin, The positive integer solutions of euler function phi(mn) = 3^k*(phi(m) + phi(n))

Crossrefs

Cf. A000010, A336385.

Programs

PARI

is(k) = fordiv(k, d, if(eulerphi(k) == 3*(eulerphi(d) + eulerphi(k/d)), return(1))); 0;