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 1-4 of 4 results.

A121519 Number of primitive roots of prime A103203(n).

Original entry on oeis.org

1, 2, 4, 8, 10, 12, 16, 22, 24, 28, 40, 52, 64, 72, 82, 84, 88, 112, 128, 130, 132, 144, 156, 172, 178, 190, 192, 232, 238, 250, 252, 276, 280, 292, 324, 358, 384, 396, 400, 418, 424, 430, 442, 448, 480, 490, 508, 520, 544, 552, 592, 612, 640, 652, 658, 682, 712
Offset: 1

Views

Author

Klaus Brockhaus, Aug 06 2006

Keywords

Comments

Also records in A008330.

Examples

			Prime A103203(5) = 23 has 10 primitive roots, so a(5) = 10; 23 = prime(9) and A008330(9) = 10 is a record in A008330.

Links

Crossrefs

Cf. A008330, A103203.

Programs

  • PARI
    r=0;for(n=1,230,k=eulerphi(prime(n)-1);if(r

A103521 Primes which have fewer primitive roots than any larger prime.

Original entry on oeis.org

3, 7, 13, 19, 31, 43, 61, 67, 79, 103, 127, 151, 211, 241, 271, 331, 421, 463, 631, 661, 691, 751, 811, 1051, 1171, 1321, 1471, 1531, 1621, 1741, 2311, 2731, 2971, 3571, 3631, 4621, 4831, 4951, 5281, 6091, 6301, 6361, 7351, 8191, 9241, 9661, 9871
Offset: 1

Views

Author

Don Reble, Mar 21 2005

Keywords

Crossrefs

Cf. A103203.

A119656 Denominator of BernoulliB(4*prime(n))/30.

Original entry on oeis.org

1, 91, 11, 29, 23, 53, 1, 1, 47, 59, 1, 149, 83, 173, 1, 107, 1, 1, 269, 1, 293, 317, 167, 179, 389, 1, 1, 1, 1, 227, 509, 263, 1, 557, 1, 1, 1, 653, 1, 347, 359, 1, 383, 773, 1, 797, 1, 1, 1, 1, 467, 479, 1, 503, 1, 1, 1, 1, 1109, 563, 1, 587, 1229, 1, 1, 1, 1, 1, 1, 1, 1, 719
Offset: 1

Views

Author

Alexander Adamchuk, Jul 28 2006

Keywords

Comments

The only composite in this sequence is a(2) = 91 = 7*13. All other a(n) are equal to 1 (for n = 1,7,8,11,15,17,18,20,26,27,28,29,33,35,36,37,39,...) or primes from A090865. Each prime from A090865 (excluding 7 and 13) appears only once in {a(n)}. The primes in {a(n)} also appear to form a subset of A103203.

Links

Crossrefs

Cf. A090865, A103203, A005385, A002445.

Programs

  • Magma
    [Denominator(Bernoulli(4*NthPrime(n)))/30: n in [1..80]]; // G. C. Greubel, Feb 10 2019
  • Mathematica
    Table[Denominator[BernoulliB[4Prime[n]]]/30,{n,1,80}]
  • PARI
    {a(n) = denominator(bernfrac(4*prime(n)))/30};
vector(80, n, a(n)) \\ G. C. Greubel and Michel Marcus, Feb 10 2019
  • Sage
    [denominator(bernoulli(4*nth_prime(n)))/30 for n in (1..80)] # G. C. Greubel, Feb 10 2019

Formula

a(n) = denominator(BernoulliB(4*prime(n)))/30.

A306371 Number of primitive roots of prime A103521(n).

Original entry on oeis.org

1, 2, 4, 6, 8, 12, 16, 20, 24, 32, 36, 40, 48, 64, 72, 80, 96, 120, 144, 160, 176, 200, 216, 240, 288, 320, 336, 384, 432, 448, 480, 576, 720, 768, 880, 960, 1056, 1200, 1280, 1344, 1440, 1664, 1680, 1728, 1920, 2112, 2208, 2304, 2400, 2592, 2784, 2880, 3072, 3456, 3840, 4224, 4320
Offset: 1

Views

Author

Jianing Song, Feb 11 2019

Keywords

Comments

Numbers k in A008330 such that no numbers <= k occur later than k in A008330.
Different from A036912 since a(19) = 144 and A036912(19) = 128.

Crossrefs

Cf. A103521.
Cf. also A103203, A121519.

Programs

  • PARI
    b(n) = if(n==1, 2, floor(exp(Euler)*n*log(log(n^2))+2.5*n/log(log(n^2))));
f(p) = my(i=0); forprime(q=p+1, b(eulerphi(p-1))+1, i+=(eulerphi(q-1)<=eulerphi(p-1))); i;
forprime(p=2, 2e4, if(f(p)==0, print1(eulerphi(p-1), ", ")))

Formula

a(n) = phi(A103521(n)-1).
Showing 1-4 of 4 results.

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