A136539 Numbers n such that n=6*phi(n)-sigma(n).

76, 1264, 327424, 5241856, 83881984, 1342160896, 343597121536

Offset: 1

Author

Farideh Firoozbakht, Jan 05 2008, Feb 01 2008

Keywords

• more
• nonn

Comments

If 5*2^n-1 is prime (that is, n is in A001770) then m = 2^n*(5*2^n-1) is in the sequence. Proof: 6*phi(m)-sigma(m) = 6*2^(n-1)*(5*2^n-2) -(2^(n+1)-1)*5*2^n = 30*2^(2n-1)-6*2^n-5*2^(2n+1)+5*2^n = 5*2^(2n)-2^n = 2^n(5*2^n-1) = m.

The first seven terms of the sequence are of such form, with n=2, 4, 8, 10, 12, 14, 18. Are all terms of the sequence of this form?

a(8) > 10^12. - Giovanni Resta, Nov 03 2012

Examples

			6*phi(76)-sigma(76)=6*36-140=76 so 76 is in the sequence.
		

Crossrefs

Cf. A001770, A136540.

Programs

Mathematica

Do[If[n==6*EulerPhi[n]-DivisorSigma[1,n],Print[n]],{n,85000000}]

Formula

a(n) = 2^k*(5*2^k-1) = A084213(k+1) with k = A001770(n), for n = 1,...,7. - M. F. Hasler, Nov 03 2012

Extensions

a(7) from Giovanni Resta, Nov 03 2012