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

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

Offset

0,1

Links

Sean A. Irvine, Table of n, a(n) for n = 0..312

Sam Wagstaff, Cunningham Project, Factorizations of 10^n+1, n<=330

Example

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

Mathematica

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} ]

Prog

(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

Crossrefs

Cf. A064131, A064132, A064133, A064134, A064136, A064137.

Sequence in context: A125915 A071472 A367120 * A332476 A179651 A139560

Adjacent sequences: A064132 A064133 A064134 * A064136 A064137 A064138

Keyword

nonn

Author

Robert G. Wilson v, Sep 10 2001

Extensions

More terms from Michel Marcus, Jul 02 2018

a(73)-a(82) from Robert Price, May 26 2019

a(73) corrected by Sean A. Irvine, May 26 2019

Status

approved