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.

Previous Showing 11-14 of 14 results.

A109050 a(n) = lcm(n, 9).

Original entry on oeis.org

0, 9, 18, 9, 36, 45, 18, 63, 72, 9, 90, 99, 36, 117, 126, 45, 144, 153, 18, 171, 180, 63, 198, 207, 72, 225, 234, 27, 252, 261, 90, 279, 288, 99, 306, 315, 36, 333, 342, 117, 360, 369, 126, 387, 396, 45, 414, 423, 144, 441, 450, 153, 468, 477, 54, 495, 504
Offset: 0

Views

Author

Mitch Harris, Jun 18 2005

Keywords

Links

Crossrefs

Cf. A106610, A109012, A109042.

Programs

Formula

a(n) = n*9/gcd(n, 9).
a(n) = 9*n/A109012(n) = 9*A106610(n). - R. J. Mathar, Apr 18 2011
Sum_{k=1..n} a(k) ~ (61/18) * n^2. - Amiram Eldar, Nov 26 2022
Sum_{n>=1} (-1)^(n+1)/a(n) = 7*log(2)/27. - Amiram Eldar, Sep 08 2023

A109052 a(n) = lcm(n,11).

Original entry on oeis.org

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 11, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 22, 253, 264, 275, 286, 297, 308, 319, 330, 341, 352, 33, 374, 385, 396, 407, 418, 429, 440, 451, 462, 473, 44, 495, 506, 517, 528, 539, 550, 561, 572, 583
Offset: 0

Views

Author

Mitch Harris, Jun 18 2005

Keywords

Links

Crossrefs

Cf. A106612, A109014, A109042.

Programs

Formula

a(n) = n*11/gcd(n, 11).
G.f.: 11*x/(1-x)^2 - 110*x^11/(1-x^11)^2. - Robert Israel, May 28 2014
From Amiram Eldar, Nov 26 2022: (Start)
a(n) = 11*A106612(n) = 11*n/A109014(n).
Sum_{k=1..n} a(k) ~ (111/22) * n^2. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 21*log(2)/121. - Amiram Eldar, Sep 08 2023

A383488 Numbers k that have at least one divisor d_i(k) for which a divisor d_j(k) exists such that d_i(k) < d_j(k) < sigma(d_i(k)).

Original entry on oeis.org

12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 99, 100, 102, 104, 105, 108, 110, 112, 114, 120, 126, 130, 132, 138, 140, 144, 150, 154, 156, 160, 162, 168, 170, 174, 176, 180, 186, 189, 192, 196, 198, 200, 204, 208, 210, 216
Offset: 1

Views

Author

Felix Huber, May 03 2025

Keywords

Comments

Numbers k (without multiplicity) that are multiples of lcm(c,i), where c is any composite and i is any integer from [c + 1, sigma(c) - 1].

Examples

			All multiples of 12 (A008594) are terms because 12 has the divisors 4 and 6 where sigma(4) = 7 > 6.
All multiples of 18 (A008600) are terms because 18 has the divisors 6 and 9 where sigma(6) = 12 > 9.
All multiples of 20 (A008602) are terms because 20 has the divisors 4 and 5 where sigma(4) = 7 > 5.

Links

Crossrefs

Supersequence of A008594, A008600, A008602, A008606, A044102, A135628.
Cf. A000203, A002808, A027750, A109042, A383360, A383489.

Programs

  • Maple
    with(NumberTheory):
A383488:=proc(n)
    option remember;
    local k,i,L;
    if n=1 then
        12
    else
        for k from procname(n-1)+1 do
            L:=Divisors(k);
            for i to nops(L)-1 do
                if sigma(L[i])>L[i+1] then
                    return k
                fi
            od
        od
    fi;
end proc;
seq(A383488(n),n=1..57);

A383489 a(n) is the number of divisors d_i(m) for which a divisor d_j(m) exists such that d_i(m) < d_j(m) < sigma(d_i(m)) where m = A383488(n).

Original entry on oeis.org

1, 1, 1, 4, 2, 5, 3, 2, 6, 2, 1, 7, 2, 1, 8, 1, 6, 7, 1, 6, 8, 1, 2, 1, 1, 1, 8, 1, 4, 1, 11, 4, 1, 7, 1, 6, 11, 5, 1, 6, 8, 3, 11, 1, 1, 3, 13, 1, 1, 10, 1, 5, 5, 6, 3, 9, 12, 4, 1, 7, 1, 6, 4, 1, 15, 1, 13, 1, 1, 4, 11, 1, 10, 1, 6, 11, 1, 1, 1, 14, 4, 2, 13
Offset: 1

Views

Author

Felix Huber, May 08 2025

Keywords

Examples

			The a(4) = 4 divisors d_i(A383488(4)) = d_i(24) are 4, 6, 8 and 12 because sigma(4) = 7 > 6, sigma(6) = 12 > 8, sigma(8) = 15 > 12 and sigma(12) = 28 > 24.

Links

Crossrefs

Cf. A000203, A002808, A027750, A109042, A383360, A383488.

Programs

  • Maple
    with(NumberTheory):
A383488:=proc(n)
    option remember;
    local k,i,L;
    if n=1 then
        12
    else
        for k from procname(n-1)+1 do
            L:=Divisors(k);
            for i to nops(L)-1 do
                if sigma(L[i])>L[i+1] then
                    return k
                fi
            od
        od
    fi;
end proc;
A383489:=proc(n)
    local a,i,L;
    L:=Divisors(A383488(n));
    a:=0;
    for i to nops(L)-1 do
        if sigma(L[i])>L[i+1] then
            a:=a+1
        fi
    od;
    return a
end proc;
seq(A383489(n),n=1..83);
Previous Showing 11-14 of 14 results.

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

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