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 A064132 Number of divisors of 5^n + 1 that are relatively prime to 5^m + 1 for all 0 < m < n. 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS From Robert Israel, Jun 26 2018: (Start) 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) LINKS Sam Wagstaff, Cunningham Project, Factorizations of 5^n-1, n odd, n<=375 MAPLE f:= n -> nops(select(t -> andmap(m -> igcd(t, 5^m+1)=1, [\$1..n-1]), numtheory:-divisors(5^n+1))): map(f, [\$0..100]); # Robert Israel, Jun 25 2018 MATHEMATICA a[n_] := Count[Divisors[5^n+1], d_ /; AllTrue[5^Range[n-1]+1, CoprimeQ[d, #]&]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 100}] (* Jean-François Alcover, Jun 27 2018 *) PROG (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 CROSSREFS Cf. A064131, A064133, A064134, A064135, A064136, A064137. Cf. A211241. Sequence in context: A300821 A194564 A284690 * A072865 A322728 A179686 Adjacent sequences:  A064129 A064130 A064131 * A064133 A064134 A064135 KEYWORD nonn AUTHOR Robert G. Wilson v, Sep 10 2001 EXTENSIONS More terms from Robert Israel, Jun 25 2018 Incorrect Mma program deleted by Editors, Jul 02 2018 STATUS approved

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Last modified September 17 06:41 EDT 2019. Contains 327119 sequences. (Running on oeis4.)