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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

Table of n, a(n) for n=1..10.

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

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Last modified October 17 07:57 EDT 2018. Contains 316276 sequences. (Running on oeis4.)