cp's OEIS Frontend

A064135 Number of divisors of 10^n + 1 that are relatively prime to 10^m + 1 for all 0 < m < n.

%I A064135 #34 May 27 2019 06:24:40
%S A064135 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,
%T A064135 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,
%U A064135 4,8,2,4,8,32,4,4,8,64,2,16,64,8,8,16,16,4
%N A064135 Number of divisors of 10^n + 1 that are relatively prime to 10^m + 1 for all 0 < m < n.
%H A064135 Sean A. Irvine, <a href="/A064135/b064135.txt">Table of n, a(n) for n = 0..312</a>
%H A064135 Sam Wagstaff, Cunningham Project, <a href="https://homes.cerias.purdue.edu/~ssw/cun/">Factorizations of 10^n+1, n<=330</a>
%e A064135 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
%t A064135 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} ]
%o A064135 (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
%Y A064135 Cf. A064131, A064132, A064133, A064134, A064136, A064137.
%K A064135 nonn
%O A064135 0,1
%A A064135 _Robert G. Wilson v_, Sep 10 2001
%E A064135 More terms from _Michel Marcus_, Jul 02 2018
%E A064135 a(73)-a(82) from _Robert Price_, May 26 2019
%E A064135 a(73) corrected by _Sean A. Irvine_, May 26 2019