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.

A238096 a(n) = Sum_{k=2..n} floor(n/k)*floor((tau(k)+1)/2), where tau = A000005.

Original entry on oeis.org

0, 1, 2, 5, 6, 10, 11, 16, 19, 23, 24, 33, 34, 38, 42, 50, 51, 60, 61, 70, 74, 78, 79, 94, 97, 101, 106, 115, 116, 129, 130, 141, 145, 149, 153, 172, 173, 177, 181, 196, 197, 210, 211, 220, 229, 233, 234, 257, 260, 269, 273, 282, 283, 298, 302, 317, 321, 325, 326, 353, 354, 358, 367, 382, 386, 399, 400, 409, 413, 426
Offset: 1

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Author

N. J. A. Sloane, Feb 22 2014

Keywords

Comments

Number of quadratic polynomials with coefficients from {1..n} for which both roots are integers.
A generalization of A006318.

Links

Crossrefs

Cf. A000005, A006318, A238097, A238098.

Formula

G.f.: Sum_{k>=2} Sum_{d|k} x^(k^2/d)/((1 - x^k)*(1 - x)). - Miles Wilson, Jun 12 2025

A238098 Number of cubic polynomials with coefficients from {1..n} for which all three roots are integers.

Original entry on oeis.org

0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 13, 15, 19, 21, 23, 25, 27, 30, 34, 36, 39, 44, 46, 49, 54, 57, 60, 64, 67, 72, 76, 79, 85, 91, 92, 95, 100, 106, 109, 115, 117, 122, 129, 132, 136, 147, 150, 154, 159, 163, 166, 174, 180, 187, 191, 194, 199, 210, 211, 216
Offset: 1

Views

Author

N. J. A. Sloane, Feb 22 2014

Keywords

Comments

A generalization of A006218 and A238096.

Links

Crossrefs

Cf. A006218, A238096, A238097.

Programs

  • PARI
    f(n) = if( n<1, 0, sum(a1=1, n, sum(a2=1, n, sum(a3=1, n, vecmax([a1, a2, a3]) == n && vecsum( factor( Pol([1, a1, a2, a3]))[, 2]) == 3)))); \\ A238097
a(n) = sum(k=1, n, (n\k)*f(k));
lista(nn) = my(v = vector(nn, k, f(k))); vector(nn, i, sum(k=1, i, (i\k)*v[k])); \\ Michel Marcus, Sep 28 2023

Formula

a(n) = Sum_{k=1..n} floor(n/k)*A238097(k).

A238304 Number of monic quartic polynomials with coefficients from {1..n} and maximum coefficient equal to n, for which all four roots are integers.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 0, 0, 2, 1, 0, 1, 1, 2, 1, 0, 0, 2, 1, 1, 2, 1, 0, 2, 0, 2, 2, 0, 1, 1, 1, 1, 1, 3, 0, 2, 0, 1, 2, 1, 1, 4, 1, 1, 1, 1, 0, 2, 2, 2, 2, 0, 1, 3, 1, 0, 1, 3, 1, 2, 0, 2, 2, 2, 1, 4, 1, 0, 3, 1, 0, 1, 0, 5, 2, 3, 1, 2, 2, 0, 2, 1, 1, 3, 1, 2, 2, 1, 2, 5
Offset: 1

Views

Author

Zak Seidov, Feb 24 2014

Keywords

Comments

Among first 10000 terms the largest is a(8640) = 174.
Also a(n) = 0 for n = 1,2,3,4,5,7,8,10,11,14,16,19,23,25,26,29,34,35,41,43,46,53,55,65,70,74,79,86,.. (329 terms among first 10000 terms.)

Links

Crossrefs

Cf. A238097.
Showing 1-3 of 3 results.

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

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