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 1-10 of 12 results. Next

A366685 a(n) = phi(11^n-1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

4, 32, 432, 3840, 64400, 373248, 7613424, 56217600, 765889344, 6913984000, 114117380608, 599824465920, 13796450740800, 98909341090560, 1356399209088000, 11341872916070400, 202178811399717504, 1171410130065973248, 24463636179365818512, 176391086415667200000
Offset: 1

Views

Author

Sean A. Irvine, Oct 16 2023

Keywords

Links

Crossrefs

phi(k^n-1): A053287 (k=2), A295500 (k=3), A295501 (k=4), A295502 (k=5), A366623 (k=6), A366635 (k=7), A366654 (k=8), A366663 (k=9), A295503 (k=10), this sequence (k=11), A366711 (k=12).
Cf. A000010, A024127, A366681, A366682, A366683, A366684.

Programs

  • Mathematica
    EulerPhi[11^Range[30] - 1]
  • PARI
    {a(n) = eulerphi(11^n-1)}

A366683 Number of divisors of 11^n-1.

Original entry on oeis.org

4, 16, 16, 40, 12, 192, 16, 96, 32, 96, 16, 1920, 16, 128, 96, 448, 8, 1024, 8, 480, 768, 1024, 32, 18432, 128, 512, 64, 2560, 16, 9216, 32, 2048, 512, 256, 192, 20480, 64, 512, 4096, 4608, 512, 36864, 16, 10240, 384, 2048, 32, 1376256, 128, 4096, 512, 2560
Offset: 1

Views

Author

Sean A. Irvine, Oct 16 2023

Keywords

Examples

			a(3)=16 because 11^3-1 has divisors {1, 2, 5, 7, 10, 14, 19, 35, 38, 70, 95, 133, 190, 266, 665, 1330}.

Links

Crossrefs

Cf. A024127, A000005, A366681, A366682, A366684, A366685.
Cf. A046801, A070528, A366709.

Programs

  • Maple
    a:=n->numtheory[tau](11^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[0, 11^Range[100]-1]
  • PARI
    a(n) = numdiv(11^n-1);

Formula

a(n) = sigma0(11^n-1) = A000005(A024127(n)).

A366684 Sum of the divisors of 11^n-1.

Original entry on oeis.org

18, 360, 2880, 46128, 299646, 7113600, 35893440, 686393568, 5105934720, 80436972240, 513593801496, 14266630210560, 62197735384584, 1165770116121600, 9349887314805120, 157025981601707904, 909804651298728804, 22898038082582016000, 110086362807146183340
Offset: 1

Views

Author

Sean A. Irvine, Oct 16 2023

Keywords

Examples

			a(3)=2880 because 11^3-1 has divisors {1, 2, 5, 7, 10, 14, 19, 35, 38, 70, 95, 133, 190, 266, 665, 1330}.

Links

Crossrefs

Cf. A024127, A000203, A366710, A366666, A366681, A366682, A366683, A366685.

Programs

  • Maple
    a:=n->numtheory[sigma](11^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[1, 11^Range[30]-1]

Formula

a(n) = sigma(11^n-1) = A000203(A024127(n)).

A366707 Number of distinct prime divisors of 12^n - 1.

Original entry on oeis.org

1, 2, 2, 4, 2, 5, 3, 6, 4, 4, 3, 8, 3, 6, 6, 9, 3, 9, 2, 7, 5, 5, 4, 12, 4, 7, 6, 10, 5, 13, 5, 11, 7, 6, 9, 14, 3, 6, 7, 13, 4, 13, 5, 11, 12, 8, 3, 18, 5, 10, 6, 12, 7, 16, 7, 13, 7, 8, 4, 18, 4, 8, 8, 13, 8, 16, 5, 10, 7, 14, 4, 21, 3, 7, 11, 11, 10, 17, 4
Offset: 1

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Links

Crossrefs

Cf. A024140, A001221, A046800, A133801, A102347, A250288, A252170, A366708, A366709, A366681.

Programs

  • PARI
    for(n = 1, 100, print1(omega(12^n - 1), ", "))

Formula

a(n) = omega(12^n-1) = A001221(A024140(n)).

A366686 Number of distinct prime divisors of 11^n + 1.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Oct 16 2023

Keywords

Links

Crossrefs

Cf. A034524, A001221, A366681, A102347, A366687, A366688, A366689, A366690.
Cf. A046799, A119704, A366712.

Programs

  • PARI
    for(n = 0, 100, print1(omega(11^n + 1), ", "))

Formula

a(n) = omega(11^n+1) = A001221(A034524(n)).

A366620 Number of distinct prime divisors of 6^n - 1.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 4, 4, 5, 3, 7, 3, 5, 5, 6, 5, 7, 3, 8, 4, 5, 5, 9, 4, 7, 6, 8, 2, 10, 3, 9, 6, 8, 6, 13, 6, 6, 6, 11, 3, 9, 5, 9, 10, 8, 4, 13, 5, 8, 9, 11, 4, 11, 6, 13, 7, 6, 4, 19, 4, 5, 10, 12, 8, 12, 3, 11, 8, 16, 2, 18, 5, 10, 10, 9, 6, 15, 4, 16, 8
Offset: 1

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Links

Crossrefs

Cf. A024062, A001221, A057955, A059888, A274907, A366621, A366622, A366623.
Cf. A046800, A133801, A366604, A366611, A366632, A366651, A366660, A102347, A366681, A366707.

Programs

  • PARI
    for(n = 1, 100, print1(omega(6^n - 1), ", "))

Formula

a(n) = omega(6^n-1) = A001221(A024062(n)).

A366632 Number of distinct prime divisors of 7^n - 1.

Original entry on oeis.org

2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 4, 7, 3, 6, 6, 6, 4, 7, 4, 8, 6, 6, 5, 11, 5, 5, 9, 8, 5, 10, 5, 8, 8, 5, 7, 11, 5, 6, 7, 11, 5, 11, 4, 10, 10, 6, 4, 14, 8, 8, 9, 8, 5, 12, 6, 13, 8, 6, 6, 17, 6, 8, 9, 11, 9, 13, 6, 9, 9, 15, 4, 18, 7, 7, 10, 8, 9, 13, 4, 16, 13
Offset: 1

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Links

Crossrefs

Cf. A024075, A001221, A057954, A059889, A074249, A218358, A366620, A366633, A366634, A366635.
Cf. A046800, A133801, A366604, A366611, A366620, A366651, A366660, A102347, A366681, A366707.

Programs

  • PARI
    for(n = 1, 100, print1(omega(7^n - 1), ", "))

Formula

a(n) = omega(7^n-1) = A001221(A024075(n)).

A366660 Number of distinct prime divisors of 9^n - 1.

Original entry on oeis.org

1, 2, 3, 3, 3, 5, 3, 5, 6, 5, 5, 7, 3, 6, 8, 6, 6, 9, 5, 7, 8, 8, 4, 12, 7, 6, 11, 9, 7, 12, 6, 7, 10, 9, 8, 12, 6, 8, 12, 11, 6, 14, 4, 12, 16, 7, 8, 15, 10, 12, 13, 9, 6, 15, 11, 14, 13, 10, 5, 18, 5, 10, 16, 8, 9, 15, 6, 13, 13, 15, 7, 19, 7, 10, 19, 13, 11
Offset: 1

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Links

Crossrefs

Cf. A024101, A001221, A057952, A366661, A366662, A366663.
Cf. A046800, A133801, A366604, A366611, A366620, A366632, A366651, A102347, A366681, A366707.

Programs

  • PARI
    for(n = 1, 100, print1(omega(9^n - 1), ", "))

Formula

a(n) = omega(9^n-1) = A001221(A024101(n)).
a(n) = A133801(2*n) = A133801(n) + A366580(n) - 1. - Max Alekseyev, Jan 07 2024

A366604 Number of distinct prime divisors of 4^n - 1.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 3, 4, 4, 5, 4, 6, 3, 6, 6, 5, 3, 8, 3, 7, 6, 7, 4, 9, 7, 7, 6, 8, 6, 11, 3, 7, 8, 7, 9, 12, 5, 7, 7, 9, 5, 12, 5, 10, 11, 9, 6, 12, 5, 12, 10, 10, 6, 12, 11, 11, 8, 9, 6, 15, 3, 8, 11, 9, 9, 14, 5, 10, 8, 15, 6, 17, 6, 10, 13, 11, 10, 16, 5
Offset: 1

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Links

Crossrefs

Cf. A024036, A001221, A057957, A133801, A366602, A366603.
Cf. A046800, A133801, A366611, A366620, A366632, A366651, A366660, A102347, A366681, A366707.

Programs

  • Mathematica
    PrimeNu[4^Range[100]-1] (* Paolo Xausa, Oct 14 2023 *)
  • PARI
    for(n = 1, 100, print1(omega(4^n - 1), ", "))
  • Python
    from sympy import primenu
def A366604(n): return primenu((1<<(n<<1))-1) # Chai Wah Wu, Oct 15 2023

Formula

a(n) = omega(4^n-1) = A001221(A024036(n)).
a(n) = A046800(2*n) = A046799(n) + A046800(n). - Max Alekseyev, Jan 07 2024

A366651 Number of distinct prime divisors of 8^n - 1.

Original entry on oeis.org

1, 2, 2, 4, 3, 4, 3, 6, 3, 6, 4, 8, 4, 6, 6, 9, 5, 6, 4, 11, 6, 8, 4, 12, 7, 7, 6, 12, 6, 11, 3, 12, 8, 10, 10, 12, 6, 8, 9, 15, 5, 11, 5, 14, 10, 8, 6, 17, 5, 13, 8, 16, 8, 12, 10, 17, 7, 10, 6, 21, 5, 7, 9, 15, 8, 15, 6, 19, 9, 20, 7, 18, 7, 12, 14, 16, 9
Offset: 1

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Links

Crossrefs

Cf. A024088, A001221, A057953, A366652, A366653, A366654.
Cf. A046800, A133801, A366604, A366611, A366620, A366632, A366660, A102347, A366681, A366707.

Programs

  • PARI
    for(n = 1, 100, print1(omega(8^n - 1), ", "))

Formula

a(n) = omega(8^n-1) = A001221(A024088(n)).
a(n) = A046800(3*n). - Max Alekseyev, Jan 09 2024
Showing 1-10 of 12 results. Next

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