A273800 Numbers n for which n = phi(x)*phi(y), where n = x + y and phi(x) is the Euler totient function of x.

8, 12, 16, 24, 32, 36, 48, 96, 128, 160, 192, 288, 768, 1152, 2048, 2560, 3072, 27648, 110592, 192704, 196608, 202496, 232448, 370688, 379904, 394264, 443512, 466048, 508672, 524288, 553120, 571008, 586016, 607744, 624704, 650624, 655360, 675584, 681856

Offset: 1

Author

Paolo P. Lava, May 31 2016

Keywords

• nonn

Examples

			8 = 3+5 = phi(3)*phi(5) = 2*4;
12 = 3+9 = phi(3)*phi(9) = 2*6;
24 = 3+21 = phi(3)*phi(21) = 2*12 or 24 = 10+14 = phi(10)*phi(14) = 4*6.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A273801.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,k,n; for n from 1 to q do
for k from 1 to trunc(n/2) do if phi(k)*phi(n-k)=n then print(n); break; fi;
od; od; end: P(10^9);

PARI

is(n)=for(x=1,n\2, if(eulerphi(x)+eulerphi(n-x)==n, return(1))); 0 \\ Charles R Greathouse IV, Jun 07 2016

Extensions

a(19)-a(39) from Giovanni Resta, May 31 2016