A092591 Exponents n such that 1-A065395(2^n) is a power of 2, where A065395(n) = sigma(phi(n)) - phi(sigma(n)).

1, 2, 3, 4, 6, 7, 12, 15, 16, 18, 30, 31, 60, 88, 106, 126, 520, 606

Offset

1,2

Comments

A000043(k) - 1 is a term for all k >= 1. - Amiram Eldar, Aug 22 2019

No more terms below 1206. - Amiram Eldar, Aug 23 2019

Links

Table of n, a(n) for n=1..18.

Example

At exponents n=1, 3, 7, 15, 31: 1-A065395(2^n)=2.
While at n=2, 4, 6, 12, 16, 18, 30, 60, 88, 106, 126: 1-A065395(2^n)=2^n.

Mathematica

f[n_] := DivisorSigma[1, EulerPhi[n]] - EulerPhi[DivisorSigma[1, n]]; pow2Q[n_] := n == 2^IntegerExponent[n, 2]; aQ[n_] := pow2Q[1 - f[2^n]]; Select[Range[130], aQ] (* Amiram Eldar, Aug 22 2019 *)

Prog

(PARI) f(n) = sigma(eulerphi(n)) - eulerphi(sigma(n)); \\ A065395
ispp2(k) = isprimepower(k, &p) && (p==2);
isok(n) = ispp2(1-f(2^n)); \\ Michel Marcus, Aug 22 2019

Crossrefs

Cf. A000010, A000203, A000043, A065395, A092584-A092590.

Sequence in context: A018534 A018276 A057732 * A287924 A039947 A339591

Adjacent sequences: A092588 A092589 A092590 * A092592 A092593 A092594

Keyword

nonn,more

Author

Labos Elemer, Mar 03 2004

Extensions

Name and example edited by Michel Marcus, Aug 22 2019

a(17)-a(18) from Amiram Eldar, Aug 23 2019

Status

approved