cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

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

Original entry on oeis.org

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

Views

Author

Robert G. Wilson v, Sep 10 2001

Keywords

Examples

			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

Links

Crossrefs

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

Programs

  • 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} ]
  • 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

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

A064136 Number of divisors of 11^n + 1 that are relatively prime to 11^m + 1 for all 0 < m < n.

Original entry on oeis.org

2, 6, 2, 2, 2, 2, 4, 2, 4, 2, 2, 16, 4, 8, 8, 4, 4, 8, 2, 16, 4, 2, 4, 16, 16, 4, 2, 4, 16, 8, 2, 16, 8, 16, 16, 48, 8, 4, 4, 8, 4, 8, 4, 4, 16, 8, 16, 16, 4, 16, 8, 8, 2, 16, 16, 32, 16, 8, 16, 16, 4, 8, 4, 16, 4, 8, 4, 64, 32, 32, 4, 8, 8, 32, 64, 8, 16, 16, 64, 16, 128, 8, 8
Offset: 0

Views

Author

Robert G. Wilson v, Sep 10 2001

Keywords

Links

Crossrefs

Cf. A064131, A064132, A064133, A064134, A064135, A064137.

Programs

  • Mathematica
    a = {1}; Do[ d = Divisors[ 11^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[ 11^n + 1 ] ][ [ 1 ] ] ] ] ], {n, 0, 55} ]
  • PARI
    a(n) = if (n==0, 2, sumdiv(11^n+1, d, vecsum(vector(n-1, k, gcd(d, 11^k+1) == 1)) == n-1)); \\ Michel Marcus, Jun 24 2018

Extensions

a(1) corrected and more terms from Michel Marcus, Jul 02 2018
a(71)-a(82) from Robert Price, May 26 2019

A064131 Number of divisors of 3^n + 1 that are relatively prime to 3^m + 1 for all 0 < m < n.

Original entry on oeis.org

2, 3, 2, 2, 2, 2, 2, 2, 4, 4, 2, 4, 2, 2, 4, 4, 2, 8, 2, 4, 2, 4, 4, 2, 8, 4, 4, 4, 4, 8, 2, 4, 2, 4, 4, 2, 2, 8, 4, 16, 4, 4, 4, 2, 8, 4, 4, 8, 4, 4, 8, 8, 4, 4, 2, 4, 8, 8, 4, 4, 8, 4, 8, 16, 2, 2, 2, 4, 8, 32, 8, 32, 4, 4, 8, 16, 16, 2, 4, 8, 8, 32, 8, 16, 32, 8, 32, 32, 8, 8, 4
Offset: 0

Views

Author

Robert G. Wilson v, Sep 10 2001

Keywords

Links

Crossrefs

Cf. A064132, A064133, A064134, A064135, A064136, A064137.

Programs

  • Mathematica
    a[0]=2; a[n_] := Length@ Select[Divisors[3^n+1], GCD[Times @@ (3^Range[1, n-1] + 1), #] == 1 &]; Array[a, 91, 0] (* Giovanni Resta, Jul 02 2018 *)
  • PARI
    a(n) = if (n==0, 2, sumdiv(3^n+1, d, vecsum(vector(n-1, k, gcd(d, 3^k+1) == 1)) == n-1)); \\ Michel Marcus, Jun 24 2018

Extensions

a(1) corrected and extended by Michel Marcus, Jul 02 2018

A064133 Number of divisors of 6^n + 1 that are relatively prime to 6^m + 1 for all 0 < m < n.

Original entry on oeis.org

2, 2, 2, 2, 2, 4, 4, 4, 4, 2, 4, 2, 2, 8, 4, 2, 8, 4, 8, 4, 4, 2, 8, 4, 4, 2, 8, 4, 16, 8, 16, 2, 8, 8, 4, 32, 8, 8, 4, 16, 8, 8, 4, 2, 4, 2, 16, 2, 16, 4, 8, 16, 8, 16, 16, 8, 16, 8, 4, 2, 4, 4, 2, 8, 8, 4, 32, 16, 16, 4, 4, 8, 2, 32, 8, 16, 16, 2, 16, 32, 8
Offset: 0

Views

Author

Robert G. Wilson v, Sep 10 2001

Keywords

Links

Crossrefs

Cf. A064131, A064132, A064134, A064135, A064136, A064137.

Programs

  • Mathematica
    a = {1}; Do[ d = Divisors[ 6^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[ 6^n + 1 ] ][ [ 1 ] ] ] ] ], {n, 0, 66} ]
  • PARI
    a(n) = if (n==0, 2, sumdiv(6^n+1, d, vecsum(vector(n-1, k, gcd(d, 6^k+1) == 1)) == n-1)); \\ Michel Marcus, Jun 24 2018

Extensions

a(67)-a(80) from Giovanni Resta, Jun 26 2018

A064134 Number of divisors of 7^n + 1 that are relatively prime to 7^m + 1 for all 0 < m < n.

Original entry on oeis.org

2, 4, 3, 2, 2, 4, 4, 4, 4, 2, 4, 4, 8, 4, 2, 2, 4, 2, 2, 4, 4, 4, 8, 2, 2, 2, 4, 2, 16, 2, 4, 8, 8, 4, 8, 16, 8, 4, 2, 8, 8, 16, 2, 128, 8, 16, 16, 2, 8, 128, 16, 8, 8, 16, 8, 32, 32, 8, 16, 16, 4, 2, 8, 32, 8, 4, 16, 8, 8, 8, 8, 4, 32, 8, 2, 8, 32, 32, 4, 16, 8, 16
Offset: 0

Views

Author

Robert G. Wilson v, Sep 10 2001

Keywords

Links

Crossrefs

Cf. A064131, A064132, A064133, A064135, A064136, A064137.

Programs

  • Mathematica
    a = {1}; Do[ d = Divisors[ 7^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[ 7^n + 1 ] ][ [ 1 ] ] ] ] ], {n, 0, 53} ]
  • PARI
    a(n) = if (n==0, 2, sumdiv(7^n+1, d, vecsum(vector(n-1, k, gcd(d, 7^k+1) == 1)) == n-1)); \\ Michel Marcus, Jun 24 2018

Extensions

a(1) corrected and more terms from Michel Marcus, Jul 02 2018

A064137 Number of divisors of 12^n + 1 that are relatively prime to 12^m + 1 for all 0 < m < n.

Original entry on oeis.org

2, 2, 4, 4, 4, 2, 2, 4, 8, 4, 2, 2, 4, 8, 4, 8, 4, 4, 4, 8, 16, 8, 16, 8, 8, 16, 8, 32, 2, 4, 2, 4, 4, 32, 4, 2, 8, 8, 8, 16, 2, 16, 2, 16, 4, 8, 2, 16, 8, 4, 32, 16, 8, 16, 32, 16, 64, 16, 32, 32, 4, 16, 16, 16, 32, 8, 16, 8, 8, 64, 16, 4, 16, 16, 64, 64, 8, 4, 8
Offset: 0

Views

Author

Robert G. Wilson v, Sep 10 2001

Keywords

Links

Crossrefs

Cf. A064131, A064132, A064133, A064134, A064135, A064136.

Programs

  • Mathematica
    a = {1}; Do[ d = Divisors[ 12^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[ 12^n + 1 ] ][ [ 1 ] ] ] ] ], {n, 0, 48} ]
  • PARI
    a(n) = if (n==0, 2, sumdiv(12^n+1, d, vecsum(vector(n-1, k, gcd(d, 12^k+1) == 1)) == n-1)); \\ Michel Marcus, Jun 24 2018

Extensions

More terms from Michel Marcus, Jul 02 2018
Showing 1-6 of 6 results.

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