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

76, 1264, 327424, 5241856, 83881984, 1342160896, 343597121536, 344413645074496

Offset

1,1

Comments

If 5*2^j-1 is prime (that is, j is in A001770) then m = 2^j*(5*2^j-1) is in the sequence. Proof: 6*phi(m)-sigma(m) = 6*2^(j-1)*(5*2^j-2) -(2^(j+1)-1)*5*2^j = 30*2^(2j-1)-6*2^j-5*2^(2j+1)+5*2^j = 5*2^(2j)-2^j = 2^j(5*2^j-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) is not of that form. - Jud McCranie, Jan 24 2026

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

a(9) > 10^15. - Jud McCranie, Jan 24 2026

Links

Table of n, a(n) for n=1..8.

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

Example

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

Mathematica

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

Crossrefs

Cf. A001770, A136540.

Sequence in context: A156396 A233365 A264627 * A267797 A163710 A293310

Adjacent sequences: A136536 A136537 A136538 * A136540 A136541 A136542

Keyword

more,nonn

Author

Farideh Firoozbakht, Jan 05 2008, Feb 01 2008

Extensions

a(7) from Giovanni Resta, Nov 03 2012

a(8) from Jud McCranie, Jan 24 2026

Status

approved