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.

A377949 Numbers k such that k | A377484(k) and (k+1) | A377484(k+1).

Original entry on oeis.org

156519, 245024, 310155, 524799, 638000, 893024, 1079000, 2055780, 2095975, 2203200, 2566025, 2592512, 2853135, 2934063, 3213375, 3294719, 4056975, 4322240, 4471935, 5746455, 6515145, 7289919, 7316000, 7329608, 7866495, 8459360, 8555624, 8934464, 9035415, 11291091
Offset: 1

Views

Author

Amiram Eldar, Nov 12 2024

Keywords

Comments

Numbers k such that k and k+1 are both terms in A056954.

Examples

			156519 is a term since A377484(156519) is divisible by 156519 and A377484(156520) is divisible by 156520.

Links

Crossrefs

Cf. A377484.
Subsequence of A056954.
Similar sequences: A355332, A377951, A377953.

Programs

  • Mathematica
    q[n_] := q[n] = Divisible[Times @@ (Rest@ Divisors[n] - 1), n]; Select[Range[10^6], q[#] && q[#+1] &]
  • PARI
    is1(k) = if(k == 1, 1, my(d = divisors(k)); !(prod(i = 2, #d, d[i]-1) % k));
lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}

A377951 Numbers k such that k | A057643(k) and (k+1) | A057643(k+1).

Original entry on oeis.org

1, 799799, 1204280, 2460975, 3382379, 6116175, 7050120, 8070699, 13339424, 20966049, 28460600, 41265680, 41463135, 52404624, 66108399, 68919080, 72946224, 81102944, 84479680, 102971924, 106663304, 110791736, 112375899, 115225439, 118333215, 131115984, 132073424
Offset: 1

Views

Author

Amiram Eldar, Nov 12 2024

Keywords

Comments

Numbers k such that k and k+1 are both terms in A377950.

Links

Crossrefs

Cf. A057643.
Subsequence of A377950.
Similar sequences: A355332, A377949, A377953.

Programs

  • Mathematica
    q[n_] := q[n] = Divisible[LCM @@ (Divisors[n] + 1), n]; Select[Range[4*10^6], q[#] && q[# + 1] &]
  • PARI
    is1(k) = !(lcm(apply(x->x+1, divisors(k))) % k);
lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}

A377952 Numbers k that divide A084190(k) = lcm{d-1 : d > 1 and d|k}.

Original entry on oeis.org

1, 30, 60, 90, 105, 132, 180, 210, 252, 264, 360, 380, 420, 495, 504, 520, 528, 546, 630, 660, 756, 840, 858, 870, 924, 990, 1040, 1056, 1092, 1140, 1224, 1260, 1320, 1365, 1485, 1512, 1530, 1560, 1638, 1656, 1716, 1722, 1740, 1785, 1820, 1848, 1900, 1980, 2040
Offset: 1

Views

Author

Amiram Eldar, Nov 12 2024

Keywords

Comments

After the first term a(1) = 1, the next odd term is a(5) = 105, the next term that is coprime to 6 is a(133) = 6545, and the next term that is coprime to 30 is a(322) = 19019.

Links

Crossrefs

Cf. A084190.
A377953 is a subsequence.
Similar sequences: A056954, A355331, A377950.

Programs

  • Mathematica
    Select[Range[2000], # == 1 || Divisible[LCM @@ (Rest @ Divisors[#] - 1), #] &]
  • PARI
    is(k) = !(lcm(apply(x -> if(x > 1, x-1, x), divisors(k))) % k);

A378059 Numbers k such k | A378056(k) and (k+1) | A378056(k+1).

Original entry on oeis.org

112375899, 871651143, 1525038515, 3524721824, 6058144224, 7616307699, 7929320399, 9778346864, 10799650575, 11536526000, 13663711775, 20596306224, 22326106256, 24442111385, 26385908912, 27394105760, 28476579725, 31552570400, 34148839725, 36045427040, 40916036304, 44037977984, 44430326199
Offset: 1

Views

Author

Amiram Eldar, Nov 15 2024

Keywords

Crossrefs

Intersection of A377951 and A377953.
Subsequence of A378058.
Cf. A378055, A378056.

Programs

  • PARI
    is1(k) = {my(d = divisors(k)); !(lcm(apply(x->x+1, d)) % k) && !(lcm(apply(x -> if(x > 1, x-1, x), d)) % k);}
lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.