A099650 Solutions to x+phi(x) = sigma(x)/2.

456, 828, 7584, 33462, 1596048, 1964544, 19800384, 26211264, 31451136, 106805184, 156868224, 316113024, 502349274, 503291904, 1557940992, 8024671392, 8052965376, 11697091872, 22149447168, 87877745664, 443520605184, 626058783744

Offset: 1

Author

Labos Elemer, Nov 05 2004

Keywords

• nonn

Comments

If 5*2^n-1 is prime then m=3*2^(n+1)*(5*2^n-1) is in the sequence because m+phi(m)=2^(n+1)*3*(5*2^n-1)+2^(n+1)*(5*2^n-2)=2^(n+1) *(20*2^n-5)=2^(n+1)*5*(2^(n+2)-1)=1/2*4*(2^(n+2)-1)*(5*2^n)= 1/2*sigma(3)*sigma(2^(n+1))*sigma(5*2^n-1)=1/2*sigma(3*2^(n+1) *(5*2^n-1))=1/2*sigma(m). So 3*2^(A001770+1)*(5*2^A001770-1) is a subsequence of this sequence. A110084 is this subsequence. Next term is greater than 10^8. - Farideh Firoozbakht, Aug 04 2005

a(23) > 10^12. - Donovan Johnson, Feb 29 2012

Examples

			n=456: phi(456) = 144, sigma(456) = 1200.
		

Crossrefs

Cf. A000010, A000203, A001770, A110084.

Programs

Mathematica

Do[If[DivisorSigma[1, m] == 2m + 2 EulerPhi[m], Print[m]], {m, 100000000}] (Firoozbakht)

Extensions

Two more terms from Farideh Firoozbakht, Aug 04 2005

a(10)-a(22) from Donovan Johnson, Feb 29 2012