This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A277208 Numbers n such that n-1 = (tau(n-1)-1)^k for some k>=0. 0
 2, 5, 17, 28, 3126, 3376, 65537, 823544, 3748097, 52521876 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS tau(n) is the number of positive divisors of n (A000005). Corresponding pairs of numbers (tau(n-1)-1, k): (0, 0); (2, 2); (4, 2); (3, 3); (5, 5); (15, 3); (16, 4); (7, 7); ... Numbers from A125137 (numbers of the form p^p + 1 where p = prime) are terms: 285311670612, 302875106592254, 827240261886336764178, 1978419655660313589123980, 20880467999847912034355032910568, ... Prime terms are in A258429: 2, 5, 17, 65537, ... Fermat prime from A019434 of the form F(n) = 2^(2^n) + 1 is term if k = 2^n * log(2) / log(2^n) is a integer. a(11), if it exists, is > 10^10. - Lars Blomberg, Nov 14 2016 LINKS EXAMPLE Number 3376 is in sequence because 3375 = (tau(3375)-1)^3 = 15^3. PROG (MAGMA) Set(Sort([n: n in[2..1000000], k in [0..20] |  (n-1) eq (NumberOfDivisors(n-1)-1)^k])) (PARI) isok(n) = {if (n==2, return(1)); my(dd = numdiv(n-1) - 1); if (dd > 1, my(k = 1); while(dd^k < n-1, k++); dd^k == n-1; ); } \\ Michel Marcus, Oct 11 2016 CROSSREFS Cf. A000005, A019434, A125137, A258429. Sequence in context: A024594 A106215 A211548 * A077217 A243183 A195271 Adjacent sequences:  A277205 A277206 A277207 * A277209 A277210 A277211 KEYWORD nonn,more AUTHOR Jaroslav Krizek, Oct 10 2016 EXTENSIONS a(9)-a(10) from Michel Marcus, Oct 11 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 19 05:41 EST 2019. Contains 319304 sequences. (Running on oeis4.)