

A064135


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


7



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

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(n1, k, gcd(d, 10^k+1) == 1)) == n1)); \\ Michel Marcus, Jun 24 2018


CROSSREFS

Cf. A064131, A064132, A064133, A064134, A064136, A064137.
Sequence in context: A096445 A125915 A071472 * A179651 A139560 A192095
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



