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A064132
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Number of divisors of 5^n + 1 that are relatively prime to 5^m + 1 for all 0 < m < n.
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6
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2, 4, 2, 2, 2, 2, 2, 4, 4, 2, 4, 8, 2, 4, 2, 4, 4, 4, 4, 8, 4, 8, 4, 4, 2, 4, 4, 8, 2, 4, 4, 8, 8, 4, 16, 4, 8, 8, 4, 4, 4, 16, 4, 16, 2, 2, 2, 8, 4, 8, 8, 16, 8, 8, 2, 2, 16, 4, 2, 16, 2, 16, 4, 16, 8, 8, 4, 2, 32, 8, 4, 8, 4, 8, 8, 16, 8, 4, 16, 16, 8, 8, 16, 8, 8, 16, 8, 8, 16, 8, 8, 4, 4, 8, 16, 8, 8, 32, 16, 2, 16
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OFFSET
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0,1
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COMMENTS
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a(n) = Product_{j: A211241(j)=2*n} (1 + e_j) where e_j is the Prime(j)-adic valuation of 5^n+1. In most cases, each e_j = 1 and a(n) is a power of 2, but a(20243) is divisible by 3 since the multiplicative order of 5 mod 40487 is 40486 and 5^20243+1 is divisible by 40487^2.
(End)
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LINKS
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MAPLE
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f:= n -> nops(select(t -> andmap(m -> igcd(t, 5^m+1)=1, [$1..n-1]), numtheory:-divisors(5^n+1))):
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MATHEMATICA
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a[n_] := Count[Divisors[5^n+1], d_ /; AllTrue[5^Range[n-1]+1, CoprimeQ[d, #]&]];
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PROG
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(PARI) a(n) = if (n==0, 2, sumdiv(5^n+1, d, vecsum(vector(n-1, k, gcd(d, 5^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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Incorrect Mma program deleted by Editors, Jul 02 2018
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STATUS
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approved
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