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.

A057952 Number of prime factors of 9^n - 1 (counted with multiplicity).

Original entry on oeis.org

3, 5, 5, 7, 6, 8, 5, 10, 8, 10, 7, 11, 5, 9, 11, 12, 8, 12, 7, 13, 11, 11, 6, 17, 10, 9, 13, 13, 9, 17, 8, 14, 12, 12, 11, 16, 8, 11, 15, 18, 8, 18, 6, 16, 19, 10, 10, 21, 12, 18, 15, 13, 8, 18, 15, 19, 15, 13, 7, 24, 7, 13, 19, 16, 12, 18, 8, 17, 15, 20, 9, 24, 9, 13, 22, 17, 13, 22
Offset: 1

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Author

Patrick De Geest, Nov 15 2000

Keywords

Links

Crossrefs

bigomega(b^n-1): A046051 (b=2), A057958 (b=3), A057957 (b=4), A057956 (b=5), A057955 (b=6), A057954 (b=7), A057953 (b=8), this sequence (b=9), A057951 (b=10), A366682 (b=11), A366708 (b=12).
Cf. A001222, A002591, A024101, A074477, A085034, A133801, A274909, A366660, A366661, A366662.

Programs

  • Mathematica
    PrimeOmega[Table[9^n - 1, {n, 1, 30}]] (* Amiram Eldar, Feb 02 2020 *)

Formula

Mobius transform of A085034. - T. D. Noe, Jun 19 2003
a(n) = A001222(A024101(n)) = A057958(2*n). - Amiram Eldar, Feb 02 2020
a(n) = A057941(n) + A057958(n). - Max Alekseyev, Jan 07 2024

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)).

A366681 Number of distinct prime divisors of 11^n - 1.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Oct 16 2023

Keywords

Links

Crossrefs

Cf. A024127, A001221, A274910, A366682, A366683, A366684, A366685.
Cf. A046800, A133801, A102347, A366707.

Programs

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

Formula

a(n) = omega(11^n-1) = A001221(A024127(n)).

A366708 Number of prime factors of 12^n - 1 (counted with multiplicity).

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Links

Crossrefs

Cf. A024140, A001222, A046051, A057951, A057952, A057953, A057954, A057955, A057956, A057957, A057958, A250288, A252170, A366707, A366709, A366682.

Programs

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

Formula

a(n) = bigomega(12^n-1) = A001222(A024140(n)).
Showing 1-6 of 6 results.

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