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.

A383361 a(n) is the i-th smallest divisor d_i of A383360(n) for which i*d_i = A383360(n).

Original entry on oeis.org

1, 2, 5, 5, 7, 9, 7, 6, 8, 11, 13, 8, 11, 8, 17, 13, 19, 17, 23, 19, 12, 29, 23, 31, 37, 16, 29, 41, 31, 43, 47, 16, 37, 53, 20, 41, 43, 35, 59, 61, 47, 25, 67, 21, 53, 71, 73, 28, 59, 79, 20, 61, 49, 83, 89, 67, 27, 55, 28, 71, 97, 73, 101, 103, 79, 107, 65, 109
Offset: 1

Views

Author

Felix Huber, May 03 2025

Keywords

Examples

			a(8) = 6 because 6 is the 5th smallest divisor of A383360(8) = 30 = 5*6.

Links

Crossrefs

Cf. A383360, A383362.

Programs

  • Maple
    with(NumberTheory):
A383360:=proc(n)
    option remember;
    local k,i,L;
    if n=1 then
        1
    else
        for k from procname(n-1)+1 do
            L:=Divisors(k);
            for i to tau(k) do
                if L[i]*i=k then
                    return k
                fi
            od
        od
    fi;
end proc;
A383361:=proc(n)
    local i,M;
    M:=Divisors(A383360(n));
    for i do
        if A383360(n)/i=M[i] then
            return M[i]
        fi
    od;
end proc;
seq(A383361(n),n=1..68);

Formula

a(n) = A383360(n)/A383362(n).
a(n) = A027750(A383360(n),A383362(n)).

A383362 a(n) is the number i for which i*d_i = A383360(n), where d_i is i-th smallest divisor d_i of A383360(n).

Original entry on oeis.org

1, 2, 3, 4, 3, 3, 4, 5, 4, 3, 3, 5, 4, 6, 3, 4, 3, 4, 3, 4, 7, 3, 4, 3, 3, 7, 4, 3, 4, 3, 3, 9, 4, 3, 8, 4, 4, 5, 3, 3, 4, 8, 3, 10, 4, 3, 3, 8, 4, 3, 12, 4, 5, 3, 3, 4, 10, 5, 10, 4, 3, 4, 3, 3, 4, 3, 5, 3, 4, 3, 4, 3, 4, 8, 3, 10, 4, 3, 4, 3, 5, 4, 4, 7, 3, 4
Offset: 1

Views

Author

Felix Huber, May 03 2025

Keywords

Examples

			a(8) = 5 because the 5th smallest divisor of A383360(8) = 30 = 5*6 is 6.

Links

Crossrefs

Cf. A383360, A383361.

Programs

  • Maple
    with(NumberTheory):
A383360:=proc(n)
    option remember;
    local k,i,L;
    if n=1 then
        1
    else
        for k from procname(n-1)+1 do
            L:=Divisors(k);
            for i to tau(k) do
                if L[i]*i=k then
                    return k
                fi
            od
        od
    fi;
end proc;
A383362:=proc(n)
    local i,M;
    M:=Divisors(A383360(n));
    for i do
        if A383360(n)/i=M[i] then
            return i
        fi
    od;
end proc;
seq(A383360(n),n=1..86);

Formula

a(n) = A383360(n)/A383361(n).
a(n) = A383360(n)/A027750(A383360(n),a(n)).

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);
Showing 1-4 of 4 results.

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

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