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 1-3 of 3 results.

A079079 a(n) = (prime(n)+1)*(prime(n+1)+1)/4.

Original entry on oeis.org

3, 6, 12, 24, 42, 63, 90, 120, 180, 240, 304, 399, 462, 528, 648, 810, 930, 1054, 1224, 1332, 1480, 1680, 1890, 2205, 2499, 2652, 2808, 2970, 3135, 3648, 4224, 4554, 4830, 5250, 5700, 6004, 6478, 6888, 7308, 7830, 8190, 8736, 9312, 9603, 9900, 10600
Offset: 1

Views

Author

Reinhard Zumkeller, Dec 22 2002

Keywords

Links

Crossrefs

Cf. A079080, A079081, A079082, A079095, smallest, greatest factor: A079083, A079084, number of factors: A079085, A079086, A079087, number, sum of divisors: A079088, A079089, sum of prime factors: A079090, A079091, Euler's totient: A079092, squarefree kernel: A079093, arithmetic derivative: A079094.

Programs

  • Haskell
    a079079 n = a079079_list !! (n-1)
a079079_list = map (`div` 4) $
               zipWith (*) a008864_list $ tail a008864_list
-- Reinhard Zumkeller, Oct 08 2012
  • Mathematica
    Table[(Prime[n] + 1)*(Prime[n + 1] + 1)/4, {n, 1, 50}] (* G. C. Greubel, Apr 25 2017 *)
  • PARI
    a(n)=(prime(n)+1)*(prime(n+1)+1)/4 \\ Charles R Greathouse IV, Aug 21 2011
  • Python
    from sympy import prime
def a(n): return (prime(n) + 1)*(prime(n + 1) + 1)/4 # Indranil Ghosh, Apr 26 2017

A079080 a(n) = gcd((prime(n)+1)*(prime(n+1)+1)/4, prime(n)*prime(n+1)+1).

Original entry on oeis.org

1, 2, 12, 6, 6, 3, 18, 6, 4, 60, 4, 3, 42, 6, 4, 2, 30, 2, 6, 36, 8, 6, 2, 3, 3, 204, 6, 54, 3, 48, 6, 2, 138, 6, 300, 4, 2, 6, 4, 2, 90, 12, 96, 3, 396, 10, 14, 6, 114, 3, 8, 120, 6, 2, 4, 4, 540, 4, 3, 282, 6, 6, 6, 156, 3, 6, 2, 6, 174, 3, 4, 6, 4, 2, 6, 4, 3, 3, 15, 6, 210, 12, 216, 4, 6, 2
Offset: 1

Views

Author

Reinhard Zumkeller, Dec 22 2002

Keywords

Links

Crossrefs

Cf. A023523, A079079, A079081, A079082.

Programs

  • Haskell
    a079080 n = a079079 n `gcd` a023523 (n + 1)
-- Reinhard Zumkeller, Oct 09 2012
  • Mathematica
    a[n_] := Module[{p = Prime[n], q}, q = NextPrime[p]; GCD[(p+1) * (q+1) / 4, p*q + 1]]; Array[a, 100] (* Amiram Eldar, Apr 06 2025 *)
  • PARI
    a(n) = my(p = prime(n), q = nextprime(p+1)); gcd((p+1)*(q+1)/4, p*q+1); \\ Amiram Eldar, Apr 06 2025

Formula

a(n) = gcd(A079079(n), A023523(n+1)).

A079082 Denominator of (prime(n)+1)*(prime(n+1)+1)/(4*(prime(n)*prime(n+1)+1)).

Original entry on oeis.org

7, 8, 3, 13, 24, 74, 18, 73, 167, 15, 287, 506, 42, 337, 623, 1564, 120, 2044, 793, 144, 721, 1093, 3694, 2878, 3266, 51, 1837, 216, 4106, 299, 2773, 8974, 138, 3452, 75, 5927, 12796, 4537, 7223, 15484, 360, 2881, 384, 12674, 99, 4199, 3361, 8437, 456
Offset: 1

Views

Author

Reinhard Zumkeller, Dec 22 2002

Keywords

Links

Crossrefs

Numerator = A079081.
Cf. A023523, A079079, A079080.

Programs

  • Haskell
    a079082 n = a079082_list !! (n-1)
a079082_list = zipWith div (tail a023523_list) a079080_list
-- Reinhard Zumkeller, Oct 09 2012
  • Mathematica
    ((#[[1]]+1)(#[[2]]+1))/(4(Times@@#+1))&/@Partition[Prime[Range[50]],2,1]//Denominator (* Harvey P. Dale, Jan 01 2018 *)
  • PARI
    a(n) = my(p = prime(n), q = nextprime(p+1)); denominator((p+1) * (q+1) / (4 * (p*q + 1))); \\ Amiram Eldar, Apr 06 2025

Formula

a(n) = denominator(A079079(n)/A023523(n+1)).
a(n) = A023523(n+1)/A079080(n).
Showing 1-3 of 3 results.

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