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A064123 Number of divisors of 5^n - 1 that are relatively prime to 5^m - 1 for all 0 < m < n. 1

%I

%S 3,2,2,2,4,2,2,2,4,2,2,2,2,4,4,4,4,2,8,4,4,8,4,2,16,4,16,2,8,4,4,4,4,

%T 4,16,4,8,8,4,4,4,8,4,4,8,4,2,2,2,4,8,4,8,8,16,2,2,4,4,4,8,8,8,8,8,4,

%U 32,16,16,4,4,8,8,8,32,4,8,4,8,4,4,16,8,4,8,16,8,2,64,2,4,2,8,8,16,4,8,8

%N Number of divisors of 5^n - 1 that are relatively prime to 5^m - 1 for all 0 < m < n.

%H Harry J. Smith, <a href="/A064123/b064123.txt">Table of n, a(n) for n = 1..119</a>

%H Sam Wagstaff, Cunningham Project, <a href="https://homes.cerias.purdue.edu/~ssw/cun/">Factorizations of 5^n-1, n odd, n<376</a>

%t a = {1}; Do[ d = Divisors[ 5^n - 1 ]; l = Length[ d ]; c = 0; k = 1; While[ k < l + 1, If[ Union[ GCD[ a, d[ [ k ] ] ] ] == {1}, c++ ]; k++ ]; Print[ c ]; a = Union[ Flatten[ Append[ a, Transpose[ FactorInteger[ 5^n - 1 ] ][ [ 1 ] ] ] ] ], {n, 1, 58} ]

%o (PARI) { allocatemem(932245000); for (n=1, 119, d=divisors(5^n - 1); l=length(d); a=0; for (i=1, l, t=1; for (m=1, n - 1, p=5^m - 1; if (gcd(d[i], p)!=1, t=0; break)); if (t, a++)); write("b064123.txt", n, " ", a) ) } \\ _Harry J. Smith_, Sep 08 2009

%Y Cf. A063982.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Sep 10 2001

%E More terms from _Harry J. Smith_, Sep 08 2009

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Last modified January 26 23:54 EST 2022. Contains 350601 sequences. (Running on oeis4.)