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.

A244329 a(n) = floor(antisigma(n) / sigma(n)) = floor(A024816(n) / A000203(n)).

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 4, 1, 5, 3, 4, 3, 7, 3, 8, 4, 6, 6, 10, 4, 9, 7, 8, 6, 13, 5, 14, 7, 10, 10, 12, 6, 17, 11, 12, 8, 19, 8, 20, 10, 12, 14, 22, 8, 20, 12, 17, 13, 25, 11, 20, 12, 19, 18, 28, 9, 29, 19, 18, 15, 24, 14, 32, 17, 24, 16, 34, 12, 35, 23
Offset: 1

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Author

Jaroslav Krizek, Jul 08 2014

Keywords

Comments

RECORD transform of a(n) is A140475 (union of number 1 and primes >= 5).
Sequence of numbers n such that a(n) = floor(antisigma(n) / n) = A046022.
Sequence of numbers n such that a(n) = a(n+1) = A244666.

Examples

			For n = 10; a(10) = floor(A024816(10) / A000203(10)) = floor(37 / 18) = 2.

Links

Crossrefs

Cf. A000203, A000217, A024816, A046022, A140475, A244327, A244328, A244666.

Programs

  • Magma
    [Floor(((n*(n+1)div 2)-SumOfDivisors(n)) div (SumOfDivisors(n))) : n in [1..1000]];
  • Mathematica
    A244329[n_] := Floor[(n*(n + 1)/2 - #)/#] & [DivisorSigma[1, n]];
Array[A244329, 100] (* Paolo Xausa, Sep 01 2024 *)

Formula

a(n) = A244327(n) - A244328(n) for n >= 7.

A244328 a(1) = a(2) = 0; for n >= 3: a(n) = floor((n*(n+1)/2) / antisigma(n)) = floor(A000217(n) / A024816(n)).

Original entry on oeis.org

0, 0, 3, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

Jaroslav Krizek, Jul 08 2014

Keywords

Comments

Decimal expansion of 29809/900000. - Stefano Spezia, Sep 02 2024

Examples

			For n = 10; a(10) = floor(A000217(10) / A024816(10)) = floor(55 / 37) = 1.

Links

Crossrefs

Cf. A000203, A000217, A024816, A244327, A244329.

Programs

  • Magma
    [Floor((n*(n+1)div 2) div ((n*(n+1)div 2)-SumOfDivisors(n))): n in [3..1000]];
  • Mathematica
    PadRight[{0, 0, 3, 3, 1, 2}, 100, 1] (* Paolo Xausa, Sep 01 2024 *)
  • PARI
    if(n>6,1,[0, 0, 3, 3, 1, 2][n]) \\ Charles R Greathouse IV, May 15 2015

Formula

a(n) = 1 for n >= 7.
a(n) = A244327(n) - A244329(n) for n >= 7.
G.f.: x^3*(3 - 2*x^2 + x^3 - x^4)/(1 - x). - Elmo R. Oliveira, Aug 03 2024
E.g.f.: exp(x) - x - 1 + x^2*(x^4 + 60*x^2 + 240*x - 360)/720. - Stefano Spezia, Sep 02 2024

A244666 Numbers n such that floor(antisigma(n) / sigma(n)) = floor(antisigma(n+1) / sigma(n+1)).

Original entry on oeis.org

1, 2, 3, 9, 21, 33, 81, 261, 897, 1334, 1364, 2974, 4364, 14282, 26937, 46593, 64665, 74918, 79833, 92685, 145215, 147454, 161001, 162602, 166934, 289454, 347738, 383594, 422073, 430137, 440013, 443402, 445874, 621027, 649154, 655005, 1174305, 1187361, 1670955
Offset: 1

Views

Author

Jaroslav Krizek, Jul 08 2014

Keywords

Comments

Also numbers n such that floor((n*(n+1)/2) / sigma(n)) = floor(((n+1)*(n+2)/2) / sigma(n+1)).
Numbers n such that A244327(n) = A244327(n+1).
Numbers n such that A244329(n) = A244329(n+1).

Links

Crossrefs

Cf. A000203, A000217, A024816, A046022, A244327, A244328, A244329.

Programs

  • Magma
    [n: n in [1..10^6] | Floor((n*(n+1)div 2) div (SumOfDivisors(n))) eq Floor(((n+1)*(n+2)div 2) div (SumOfDivisors(n+1)))]
Showing 1-3 of 3 results.

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