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.

A072055 a(n) = 2*prime(n)+1.

Original entry on oeis.org

5, 7, 11, 15, 23, 27, 35, 39, 47, 59, 63, 75, 83, 87, 95, 107, 119, 123, 135, 143, 147, 159, 167, 179, 195, 203, 207, 215, 219, 227, 255, 263, 275, 279, 299, 303, 315, 327, 335, 347, 359, 363, 383, 387, 395, 399, 423, 447, 455, 459, 467, 479
Offset: 1

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Author

Reinhard Zumkeller, Jun 11 2002

Keywords

Links

Crossrefs

Cf. A000040, A005385, A023589, A023590, A023591, A023592, A023593, A072059, A023595, A072060, A072056, A072057, A072058, A072192, A165286, A278230.
One less than A089241. After the initial term equal to A166496.
Row 4 of A286625, column 4 of A286623.

Programs

Formula

a(n) = A089241(n)-1.

A072056 Number of divisors of 2*prime(n)+1.

Original entry on oeis.org

2, 2, 2, 4, 2, 4, 4, 4, 2, 2, 6, 6, 2, 4, 4, 2, 4, 4, 8, 4, 6, 4, 2, 2, 8, 4, 6, 4, 4, 2, 8, 2, 6, 6, 4, 4, 12, 4, 4, 2, 2, 6, 2, 6, 4, 8, 6, 4, 8, 8, 2, 2, 8, 2, 4, 4, 6, 4, 8, 2, 10, 2, 8, 4, 8, 4, 8, 12, 4, 4, 4, 2, 12, 6, 8, 4, 4, 8, 4, 12, 2, 4, 2, 6, 4, 2, 4, 8, 4, 6, 8, 4, 12
Offset: 1

Views

Author

Reinhard Zumkeller, Jun 11 2002

Keywords

Examples

			Divisors of A072055(8) = 2*A000040(8)+1 = 2*19+1=39: {1,3,13,39} with size 4, therefore a(8) = 4.

Links

Crossrefs

Cf. A000005, A000040, A072055, A072057.

Programs

  • Mathematica
    Table[DivisorSigma[0,2Prime[n]+1],{n,100}] (* Harvey P. Dale, Apr 12 2021 *)
  • PARI
    a(n) = numdiv(2*prime(n)+1); \\ Amiram Eldar, Apr 26 2024
  • PARI
    lista(pmax) = forprime(p = 2, pmax, print1(numdiv(2*p+1), ", ")); \\ Amiram Eldar, Apr 26 2024

Formula

a(n) = A000005(A072055(n)).

A247787 Sum of divisors of 2*prime(n)-1.

Original entry on oeis.org

4, 6, 13, 14, 32, 31, 48, 38, 78, 80, 62, 74, 121, 108, 128, 192, 182, 133, 160, 192, 180, 158, 288, 240, 194, 272, 252, 288, 256, 403, 288, 390, 448, 278, 480, 352, 314, 434, 494, 576, 576, 381, 512, 576, 528, 398, 422, 540, 608, 458, 768, 702, 532, 672
Offset: 1

Views

Author

Jaroslav Krizek, Sep 24 2014

Keywords

Comments

See A005382 (primes p such that sigma(2p-1) = 2p).

Examples

			For n = 3; prime(3) = 5, a(3) = sigma(2*5-1) = sigma(9) = 13.

Links

Crossrefs

Cf. A000203, A072057, A005382, A247788.

Programs

  • Magma
    [SumOfDivisors(2*p-1): p in PrimesUpTo(2000)]
  • PARI
    vector(100,n,sigma(2*prime(n)-1)) \\ Derek Orr, Sep 25 2014

Formula

a(n) = sigma(A076274(n)) = A000203(A076274(n)).
Showing 1-3 of 3 results.

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

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