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A064135
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Number of divisors of 10^n + 1 that are relatively prime to 10^m + 1 for all 0 < m < n.
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7
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2, 2, 2, 4, 4, 2, 2, 2, 4, 4, 4, 8, 2, 4, 8, 8, 32, 8, 2, 2, 4, 8, 8, 16, 2, 8, 4, 4, 4, 4, 8, 2, 16, 4, 8, 4, 8, 8, 4, 16, 4, 4, 4, 8, 4, 8, 8, 8, 16, 4, 16, 4, 4, 2, 8, 16, 8, 4, 16, 8, 2, 4, 4, 4, 8, 4, 8, 2, 4, 8, 32, 4, 4, 8, 64, 2, 16, 64, 8, 8, 16, 16, 4
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OFFSET
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0,1
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LINKS
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EXAMPLE
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1001 = 7 * 11 * 13 and has 8 divisors, but only {1, 7, 13, 91} are relatively prime to 11 and 101, so a(3) = 4. - Bernard Schott, May 27 2019
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MATHEMATICA
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a = {1}; Do[ d = Divisors[ 10^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[ 10^n + 1 ] ][ [ 1 ] ] ] ] ], {n, 0, 46} ]
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PROG
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(PARI) a(n) = if (n==0, 2, sumdiv(10^n+1, d, vecsum(vector(n-1, k, gcd(d, 10^k+1) == 1)) == n-1)); \\ Michel Marcus, Jun 24 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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