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A092591
Exponents n such that 1-A065395(2^n) is a power of 2, where A065395(n) = sigma(phi(n)) - phi(sigma(n)).
0
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
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
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