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.

Previous Showing 11-17 of 17 results.

A366666 Sum of the divisors of 9^n+1.

Original entry on oeis.org

3, 18, 126, 1332, 10476, 109926, 816732, 8906760, 64570086, 706911048, 5357742012, 56496274632, 456919958880, 4661686010664, 35152280388792, 388532214509688, 2779530283277766, 30018958465575240, 230668806145962744, 2431533550553980488, 19410628990783168944
Offset: 0

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Examples

			a(2)=126 because 9^2+1 has divisors {1, 2, 41, 82}.

Links

Crossrefs

Cf. A062396, A000203, A057935, A366662, A366664, A366665, A366667.
Cf. A069061, A366578, A366607, A366617, A366629, A366638, A366657, A366668, A366689, A366715.

Programs

  • Maple
    a:=n->numtheory[sigma](9^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[1, 9^Range[0,20] + 1] (* Paul F. Marrero Romero, Nov 14 2023 *)

Formula

a(n) = sigma(9^n+1) = A000203(A062396(n)).
a(n) = A366578(2*n). - Max Alekseyev, Jan 08 2024

A366577 Number of divisors of 3^n+1.

Original entry on oeis.org

2, 3, 4, 6, 4, 6, 8, 6, 8, 24, 12, 12, 8, 6, 16, 48, 4, 24, 16, 12, 8, 72, 16, 6, 64, 24, 16, 96, 16, 24, 48, 12, 4, 96, 16, 24, 16, 24, 16, 192, 32, 12, 128, 6, 32, 768, 16, 24, 16, 24, 128, 384, 16, 12, 32, 96, 64, 192, 16, 12, 128, 12, 32, 4608, 4, 24, 64
Offset: 0

Views

Author

Sean A. Irvine, Oct 13 2023

Keywords

Examples

			a(4)=4 because 3^4+1 has divisors {1, 2, 41, 82}.

Links

Crossrefs

Cf. A000005, A002592, A034472, A046798, A057935, A057941, A074476, A274909, A366575, A366578, A366579, A366580

Programs

  • Maple
    a:=n->numtheory[tau](3^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[0,3^Range[0,100]+1] (* Paolo Xausa, Oct 15 2023 *)
  • PARI
    a(n) = numdiv(3^n+1); \\ Michel Marcus, Oct 14 2023

Formula

a(n) = sigma0(3^n+1) = A000005(A034472(n)).

A366578 Sum of the divisors of 3^n+1.

Original entry on oeis.org

3, 7, 18, 56, 126, 434, 1332, 3836, 10476, 42560, 109926, 315112, 816732, 2790074, 8906760, 30220288, 64570086, 229156928, 706911048, 2034690952, 5357742012, 21838961760, 56496274632, 164750562956, 456919958880, 1517043139136, 4661686010664, 16489453890560
Offset: 0

Views

Author

Sean A. Irvine, Oct 13 2023

Keywords

Examples

			a(4)=126 because 3^4+1 has divisors {1, 2, 41, 82}.

Links

Crossrefs

Cf. A000203, A002592, A024023, A057935, A057941, A074476, A075708, A274909, A366576, A366577, A366579, A366580

Programs

  • Maple
    a:=n->numtheory[sigma](3^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[1,3^Range[0,30]+1] (* Paolo Xausa, Oct 15 2023 *)

Formula

a(n) = sigma(3^n+1) = A000203(A034472(n)).

A366664 Number of distinct prime divisors of 9^n + 1.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 3, 4, 2, 4, 3, 4, 6, 4, 4, 5, 2, 4, 4, 4, 5, 7, 5, 4, 4, 6, 4, 5, 6, 4, 7, 5, 2, 6, 5, 8, 8, 5, 6, 7, 5, 5, 10, 7, 6, 8, 4, 4, 6, 9, 6, 8, 7, 6, 9, 7, 9, 9, 5, 3, 11, 6, 4, 11, 6, 7, 9, 9, 7, 6, 9, 5, 6, 6, 6, 11, 4, 8, 7, 5, 4, 7, 5, 5, 11
Offset: 0

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Links

Crossrefs

Cf. A062396, A001221, A057935, A366660, A366665, A366666, A366667.
Cf. A046799, A366580, A366605, A366615, A366627, A366636, A366655, A119704, A366686, A366712.

Programs

  • Mathematica
    PrimeNu[9^Range[0,90]+1] (* Harvey P. Dale, Jul 04 2024 *)
  • PARI
    for(n = 0, 100, print1(omega(9^n + 1), ", "))

Formula

a(n) = omega(9^n+1) = A001221(A062396(n)).
a(n) = A366580(2*n). - Max Alekseyev, Jan 08 2024

A366665 Number of divisors of 9^n+1.

Original entry on oeis.org

2, 4, 4, 8, 8, 12, 8, 16, 4, 16, 8, 16, 64, 16, 16, 48, 4, 16, 16, 16, 32, 128, 32, 16, 16, 128, 16, 32, 64, 16, 128, 32, 4, 64, 32, 384, 256, 32, 64, 128, 32, 32, 1024, 128, 64, 384, 16, 16, 64, 512, 64, 256, 128, 64, 512, 192, 512, 512, 32, 8, 2048, 64, 16
Offset: 0

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Examples

			a(2)=4 because 9^2+1 has divisors {1, 2, 41, 82}.

Links

Crossrefs

Cf. A062396, A000005, A057935, A366661, A366664, A366666, A366667.
Cf. A046798, A366577, A366606, A366616, A366628, A366637, A366656, A344897, A366688, A366714.

Programs

  • Maple
    a:=n->numtheory[tau](9^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[0, 9^Range[0,62] + 1] (* Paul F. Marrero Romero, Nov 13 2023 *)
  • PARI
    a(n) = numdiv(9^n+1);

Formula

a(n) = sigma0(9^n+1) = A000005(A062396(n)).
a(n) = A366577(2*n). - Max Alekseyev, Jan 08 2024

A366713 Number of prime factors of 12^n + 1 (counted with multiplicity).

Original entry on oeis.org

1, 1, 2, 3, 2, 2, 3, 3, 3, 5, 4, 2, 4, 5, 4, 7, 2, 3, 5, 4, 6, 9, 6, 4, 6, 6, 5, 10, 3, 3, 6, 3, 2, 9, 4, 5, 7, 4, 5, 11, 4, 5, 6, 5, 4, 12, 3, 5, 5, 5, 10, 9, 5, 5, 10, 7, 9, 11, 8, 6, 10, 5, 6, 15, 5, 9, 11, 4, 5, 12, 10, 3, 10, 5, 8, 17, 5, 6, 9, 4, 6, 15
Offset: 0

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Links

Crossrefs

Cf. A178248, A001222, A054992, A057934, A057935, A057936, A057937, A057938, A057939, A057940, A057941, A366712, A366714, A366715, A366716, A366719, A366720, A366708, A366687.

Programs

  • Mathematica
    PrimeOmega[12^Range[70]+1]
  • PARI
    a(n)=bigomega(12^n+1)

Formula

a(n) = bigomega(12^n+1) = A001222(A178248(n)).

A366687 Number of prime factors of 11^n + 1 (counted with multiplicity).

Original entry on oeis.org

1, 3, 2, 5, 2, 4, 4, 4, 3, 7, 3, 7, 4, 6, 5, 8, 3, 6, 5, 7, 4, 7, 4, 7, 7, 6, 3, 10, 6, 6, 6, 7, 4, 13, 6, 11, 7, 5, 4, 11, 5, 6, 9, 5, 6, 13, 6, 7, 5, 8, 6, 11, 3, 7, 9, 13, 7, 12, 6, 7, 8, 6, 4, 13, 3, 10, 8, 9, 7, 14, 8, 6, 10, 8, 8, 13, 6, 12, 12, 7, 10
Offset: 0

Views

Author

Sean A. Irvine, Oct 16 2023

Keywords

Links

Crossrefs

Cf. A034524, A001222, A057934, A062308, A366686, A366688, A366689, A366690.
Cf. A054992, A057941, A057940, A057939, A057938, A057937, A057936, A057935, A057934, A366713.

Programs

  • Mathematica
    PrimeOmega[11^Range[70]+1]
  • PARI
    a(n)=bigomega(11^n+1)

Formula

a(n) = bigomega(11^n+1) = A001222(A034524(n)).
Previous Showing 11-17 of 17 results.

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