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A277208
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Numbers n such that n-1 = (tau(n-1)-1)^k for some k>=0, where tau(n) is the number of divisors of n (A000005).
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0
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OFFSET
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1,1
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COMMENTS
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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, ...
A Fermat prime from A019434 of the form F(n) = 2^(2^n) + 1 is a term if k = 2^n * log(2) / log(2^n) is an integer.
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LINKS
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EXAMPLE
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3376 is in the sequence because 3375 = (tau(3375)-1)^3 = 15^3.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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