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.

A058888 Number of terms in the set invphi(2*prime(n)), where prime(n) is the n-th prime.

Original entry on oeis.org

4, 4, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Labos Elemer, Jan 08 2001

Keywords

Examples

			The set invphi(2*3) = {7,9,14,18}. It has 4 terms, so a(2) = 4, while invphi(2*1601) = {3203,6406}, thus a(252) = 2.

Links

Crossrefs

Cf. A000010, A002202, A005277, A007617, A071629-A071634.

Programs

  • Maple
    with(numtheory): [seq(nops(invphi(2*ithprime(i))),i=1..256)];
  • PARI
    a(n) = invphiNum(2*prime(n)); \\ Amiram Eldar, Nov 07 2024, using Max Alekseyev's invphi.gp

Extensions

Offset corrected by Donovan Johnson, Apr 28 2013

A071629 Number of terms in the set InvPhi(4*prime(n)), where prime(n) is the n-th prime.

Original entry on oeis.org

5, 6, 5, 2, 3, 2, 0, 0, 3, 3, 0, 2, 3, 2, 0, 3, 0, 0, 2, 0, 2, 2, 3, 3, 2, 0, 0, 0, 0, 3, 2, 3, 0, 2, 0, 0, 0, 2, 0, 3, 3, 0, 3, 2, 0, 2, 0, 0, 0, 0, 3, 3, 0, 3, 0, 0, 0, 0, 2, 3, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 2, 3, 0, 3, 2, 0, 3, 0, 0, 0, 0, 0, 0, 2, 3, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Labos Elemer, May 30 2002

Keywords

Examples

			For n=5: invphi(4*11) = [69,92,138], a(5) = 3.

Links

Crossrefs

Cf. A000010, A002202, A005277, A007617, A058888, A071630-A071634.

Programs

  • Maple
    [seq(nops(invphi(4*ithprime(i))),i=1..128)];
  • PARI
    a(n) = invphiNum(4*prime(n)); \\ Amiram Eldar, Nov 07 2024, using Max Alekseyev's invphi.gp

A071630 Number of terms in the set InvPhi(8*prime(n)), where prime(n) is the n-th prime.

Original entry on oeis.org

6, 10, 9, 3, 6, 3, 2, 0, 4, 6, 0, 3, 4, 3, 0, 4, 0, 0, 3, 2, 3, 3, 4, 4, 3, 2, 0, 2, 0, 4, 3, 6, 2, 3, 2, 0, 0, 3, 0, 4, 6, 0, 4, 3, 0, 3, 0, 0, 0, 0, 4, 6, 0, 4, 0, 0, 2, 0, 3, 4, 0, 4, 3, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 3, 0, 0, 0, 0, 2, 3, 4, 0, 6, 3, 0, 4, 2, 0, 0, 0, 0, 2, 3, 6, 3, 0, 6, 0, 0, 0, 0, 2, 0, 0
Offset: 1

Views

Author

Labos Elemer, May 30 2002

Keywords

Examples

			For n=5: invphi(8*11) = {89,115,178,184,230,276}, a(5) = 6.

Links

Crossrefs

Cf. A000010, A002202, A005277, A007617, A058888, A071629-A071634.

Programs

  • Maple
    [seq(nops(invphi(8*ithprime(i))),i=1..128)];
  • PARI
    a(n) = invphiNum(8*prime(n)); \\ Amiram Eldar, Nov 07 2024, using Max Alekseyev's invphi.gp

A071631 Number of terms in the set InvPhi(16*prime(n)), where prime(n) is the n-th prime.

Original entry on oeis.org

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

Views

Author

Labos Elemer, May 30 2002

Keywords

Examples

			invphi(16*29) = {699,885,932,944,1180,1398,1416,1770} so a(10) = 8.

Links

Crossrefs

Cf. A000010, A002202, A005277, A007617, A058888, A071629-A071634.

Programs

  • Maple
    [seq(nops(invphi(16*ithprime(i))),i=1..128)];
  • PARI
    a(n) = invphiNum(16*prime(n)); \\ Amiram Eldar, Nov 07 2024, using Max Alekseyev's invphi.gp

A071632 Number of terms in the set InvPhi(1024*prime(n)), where prime(n) is the n-th prime.

Original entry on oeis.org

13, 43, 31, 24, 32, 16, 13, 8, 14, 27, 4, 24, 11, 16, 0, 18, 7, 8, 16, 19, 16, 12, 18, 19, 18, 12, 0, 14, 6, 18, 10, 23, 9, 10, 17, 8, 4, 28, 5, 11, 20, 12, 18, 22, 0, 10, 0, 6, 0, 6, 21, 32, 0, 11, 4, 0, 16, 8, 20, 19, 0, 18, 14, 3, 10, 5, 12, 16, 14, 2, 0, 26, 0, 16, 0, 0, 0, 14, 14
Offset: 1

Views

Author

Labos Elemer, May 30 2002

Keywords

Examples

			InvPhi(1024*31) = {39685,63496,79370,95244}, so a(11) = 4.
Observe that a(15) = 0 because 47 needs a very large 2^i multiplier (instead of 1024) to give a nonempty InvPhi set.

Links

Crossrefs

Cf. A000010, A002202, A005277, A007617, A058888, A071629, A071630, A071631, A071633, A071634.

Programs

  • Maple
    [seq(nops(invphi(1024*ithprime(i))),i=1..128)];
  • PARI
    a(n) = invphiNum(1024 * prime(n)); \\ Amiram Eldar, Nov 11 2024, using Max Alekseyev's invphi.gp

A071633 Number of terms in the set InvPhi(65536*prime(n)), where prime(n) is the n-th prime.

Original entry on oeis.org

19, 82, 59, 46, 56, 34, 26, 20, 31, 52, 10, 56, 24, 34, 0, 30, 20, 20, 32, 37, 32, 24, 30, 37, 34, 24, 2, 26, 16, 35, 22, 46, 15, 20, 38, 14, 20, 58, 11, 22, 42, 24, 33, 46, 3, 20, 0, 18, 10, 12, 44, 56, 0, 29, 8, 0, 31, 14, 38, 44, 0, 30, 28, 9, 24, 18, 30, 34, 29, 8, 0, 50, 6
Offset: 1

Views

Author

Labos Elemer, May 30 2002

Keywords

Examples

			invphi(65536*103) = {6750209,13500418}, so a(27) = 2.
Observe that a(15) = 0 because 47 needs very large 2^i multiplier (instead of 65536) to give nonempty InvPhi set.

Links

Crossrefs

Cf. A000010, A005277, A007617, A058888, A002202, A071629, A071630, A071631, A071632, A071634.

Programs

  • Maple
    [seq(nops(invphi(65536*ithprime(i))),i=1..128)];
  • PARI
    a(n) = invphiNum(65536 * prime(n)); \\ Amiram Eldar, Nov 11 2024, using Max Alekseyev's invphi.gp
Showing 1-6 of 6 results.

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