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

A295501 a(n) = phi(4^n-1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

2, 8, 36, 128, 600, 1728, 10584, 32768, 139968, 480000, 2640704, 6635520, 44717400, 132765696, 534600000, 2147483648, 11452896600, 26121388032, 183250539864, 473702400000, 2427720325632, 8834232287232, 45914084232320, 109586090557440, 656100000000000
Offset: 1

Views

Author

Seiichi Manyama, Nov 22 2017

Keywords

Links

Crossrefs

Cf. A000010, A053285.
phi(k^n-1): A053287 (k=2), A295500 (k=3), this sequence (k=4), A295502 (k=5), A366623 (k=6), A366635 (k=7), A366654 (k=8), A366663 (k=9), A295503 (k=10), A366685 (k=11), A366711 (k=12).
Cf. A366602, A366603, A366604, A366608.

Programs

  • Mathematica
    EulerPhi[4^Range[30] - 1] (* Paolo Xausa, Jun 17 2024 *)
  • PARI
    {a(n) = eulerphi(4^n-1)}

Formula

a(n) = n*A027695(n).
a(n) = A053287(2*n) = A053285(n) * A053287(n). - Max Alekseyev, Jan 07 2024

A366623 a(n) = phi(6^n-1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

4, 24, 168, 864, 6200, 30240, 223944, 1119744, 7457184, 37200000, 277618528, 1254113280, 10445497920, 51618196224, 365601600000, 1770091315200, 13439285266176, 62336092492800, 484935499902880, 2179146240000000, 17141125020596640, 86330728271779200
Offset: 1

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Links

Crossrefs

phi(k^n-1): A053287 (k=2), A295500 (k=3), A295501 (k=4), A295502 (k=5), this sequence (k=6), A366635 (k=7), A366654 (k=8), A366663 (k=9), A295503 (k=10), A366685 (k=11), A366711 (k=12).
Cf. A024062, A000010, A295502, A366620, A366621, A366622.

Programs

  • Mathematica
    EulerPhi[6^Range[22] - 1] (* Paul F. Marrero Romero, Oct 23 2023 *)
  • PARI
    {a(n) = eulerphi(6^n-1)}

Formula

a(n) = A000010(A024062(n)). - Paul F. Marrero Romero, Oct 23 2023

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)}

A295502 a(n) = phi(5^n-1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

2, 8, 60, 192, 1400, 4320, 39060, 119808, 894240, 2912000, 24414060, 62208000, 610351560, 1959874560, 13154400000, 44043337728, 380537036928, 997843069440, 9485297382000, 25606963200000, 230106651919200, 748687423334400, 5959800062798400, 15138938880000000
Offset: 1

Views

Author

Seiichi Manyama, Nov 22 2017

Keywords

Comments

Faye et al. prove that no term is of the form 5^k-1. - Michel Marcus, Jun 16 2024

Links

Crossrefs

Cf. A000010, A024049.
phi(k^n-1): A053287 (k=2), A295500 (k=3), A295501 (k=4), this sequence (k=5), A366623 (k=6), A366635 (k=7), A366654 (k=8), A366663 (k=9), A295503 (k=10), A366685 (k=11), A366711 (k=12).

Programs

  • Mathematica
    EulerPhi[5^Range[25] - 1] (* Paolo Xausa, Jun 18 2024 *)
  • PARI
    {a(n) = eulerphi(5^n-1)}

Formula

a(n) = n*A027741(n).
a(n) = A000010(A024049(n)). - Michel Marcus, Jun 16 2024

A366635 a(n) = phi(7^n-1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

2, 16, 108, 640, 5600, 36288, 264992, 1536000, 12387168, 85120000, 658519752, 3135283200, 32296336800, 216063877120, 1450340640000, 8333819904000, 77537969371008, 488237947481088, 3790563394976072, 19162214400000000, 170264753751665664, 1245495178700551680
Offset: 1

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Links

Crossrefs

phi(k^n-1): A053287 (k=2), A295500 (k=3), A295501 (k=4), A295502 (k=5), A366623 (k=6), this sequence (k=7), A366654 (k=8), A366663 (k=9), A295503 (k=10), A366685 (k=11), A366711 (k=12).
Cf. A000010, A024075, A366632, A366633, A366634.

Programs

  • Mathematica
    EulerPhi[7^Range[30] - 1] (* Wesley Ivan Hurt, Oct 15 2023 *)
  • PARI
    {a(n) = eulerphi(7^n-1)}

A366654 a(n) = phi(8^n-1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

6, 36, 432, 1728, 27000, 139968, 1778112, 6635520, 113467392, 534600000, 6963536448, 26121388032, 465193834560, 2427720325632, 28548223200000, 109586090557440, 1910296842179040, 9618417501143040, 123523151337020736, 406467072000000000, 7713001620195508224
Offset: 1

Views

Author

Sean A. Irvine, Oct 15 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), this sequence (k=8), A366663 (k=9), A295503 (k=10), A366685 (k=11), A366711 (k=12).
Cf. A000010, A010705, A024088, A057953, A059890, A274908, A366651, A366652, A366653.

Programs

  • Mathematica
    EulerPhi[8^Range[30] - 1]
  • PARI
    {a(n) = eulerphi(8^n-1)}
  • Python
    from sympy import totient
def A366654(n): return totient((1<<3*n)-1) # Chai Wah Wu, Oct 15 2023

Formula

a(n) = A053287(3*n). - Max Alekseyev, Jan 09 2024

A366663 a(n) = phi(9^n-1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

4, 32, 288, 2560, 26400, 165888, 2384928, 15728640, 141087744, 1246080000, 14758128000, 85996339200, 1270928131200, 8810420097024, 70207948800000, 677066362060800, 8218041445152000, 43129128265187328, 674757689572915200, 4238841176064000000
Offset: 1

Views

Author

Sean A. Irvine, Oct 15 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), this sequence (k=9), A295503 (k=10), A366685 (k=11), A366711 (k=12).
Cf. A000010, A024101, A057952, A366660, A366661, A366662, A366667.

Programs

  • Mathematica
    EulerPhi[9^Range[30] - 1]
  • PARI
    {a(n) = eulerphi(9^n-1)}

Formula

a(n) = A295500(2*n) = 2 * A295500(n) * A366579(n). - Max Alekseyev, Jan 07 2024

A366716 a(n) = phi(12^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 12, 112, 1296, 20416, 229680, 2306304, 32916240, 400515072, 3863116800, 47825825600, 685853880624, 8732596764672, 97509650382144, 990242755633152, 11148606564480000, 184883057981234176, 2047145911595946000, 20281543142263603200, 294779525244632305920
Offset: 0

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Links

Crossrefs

Cf. A178248, A000010, A366711, A366712, A366713, A366714, A366715, A366719, A366720, A366690.

Programs

  • Mathematica
    EulerPhi[12^Range[0,19] + 1] (* Paul F. Marrero Romero, Oct 27 2023 *)
  • PARI
    {a(n) = eulerphi(12^n+1)}

Formula

a(n) = A000010(A178248(n)). - Paul F. Marrero Romero, Oct 27 2023

A295500 a(n) = phi(3^n-1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 4, 12, 32, 110, 288, 1092, 2560, 9072, 26400, 84700, 165888, 797160, 2384928, 6019200, 15728640, 64533700, 141087744, 580765248, 1246080000, 4823425152, 14758128000, 46070066188, 85996339200, 385087175000, 1270928131200, 3474144608256, 8810420097024
Offset: 1

Views

Author

Seiichi Manyama, Nov 22 2017

Keywords

Links

Crossrefs

Cf. A000010, A024023, A027385.
phi(k^n-1): A053287 (k=2), this sequence (k=3), A295501 (k=4), A295502 (k=5), A366623 (k=6), A366635 (k=7), A366654 (k=8), A366663 (k=9), A295503 (k=10), A366685 (k=11), A366711 (k=12).

Programs

  • Mathematica
    EulerPhi[3^Range[30] - 1] (* Paolo Xausa, Jun 18 2024 *)
  • PARI
    {a(n) = eulerphi(3^n-1)}

Formula

a(n) = n*A027385(n).
a(n) = A000010(A024023(n)). - Michel Marcus, Jun 18 2024

A366710 Sum of the divisors of 12^n-1.

Original entry on oeis.org

12, 168, 1896, 30240, 271464, 4247040, 39156480, 636854400, 5817876000, 72749094432, 852203639280, 15743437516800, 116720110574544, 1518251476008960, 17220536137159296, 292933954031846400, 2420303924088730368, 38936041113123840000, 348523635677043192936
Offset: 1

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Examples

			a(3)=1896 because 12^3-1 has divisors {1, 11, 157, 1727}.

Links

Crossrefs

Cf. A024140, A000203, A366707, A366708, A366709, A366711, A366684.

Programs

  • Maple
    a:=n->numtheory[sigma](12^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[1, 12^Range[30]-1]

Formula

a(n) = sigma(12^n-1) = A000203(A024140(n)).
Showing 1-10 of 12 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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