A135628 -id:A135628 - cp's OEIS frontend

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)).

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

Felix Huber, May 03 2025

nonn

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].

			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.

Felix Huber, Table of n, a(n) for n = 1..10000

Supersequence of A008594, A008600, A008602, A008606, A044102, A135628.

Cf. A000203, A002808, A027750, A109042, A383360, A383489.

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);

A242570 a(n) = 252 * n.

Original entry on oeis.org

0, 252, 504, 756, 1008, 1260, 1512, 1764, 2016, 2268, 2520, 2772, 3024, 3276, 3528, 3780, 4032, 4284, 4536, 4788, 5040, 5292, 5544, 5796, 6048, 6300, 6552, 6804, 7056, 7308, 7560, 7812, 8064, 8316, 8568, 8820, 9072, 9324, 9576, 9828, 10080, 10332, 10584, 10836, 11088, 11340

Offset: 0

Derek Orr, May 17 2014

As lcm(1,2,3,...,9) = 2520, 10*a(n) + k is divisible by each k from 1 through 9.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A001477, A008600, A008603, A008589, A008591, A008594, A008596.

Cf. A044102, A135628.

252*Range[0, 49] (* Alonso del Arte, May 17 2014 *)
LinearRecurrence[{2,-1},{0,252},50] (* Harvey P. Dale, Mar 25 2025 *)

PARI
```
for(n=0,50,print(252*n))
```

From Elmo R. Oliveira, Apr 16 2024: (Start)
G.f.: 252*x/(x-1)^2.
E.g.f.: 252*x*exp(x).
a(n) = 2*a(n-1) - a(n-2) for n >= 2.
a(n) = 7*A044102(n) = 9*A135628(n) = 12*A008603(n) = 14*A008600(n) = 18*A008596(n) = 21*A008594(n) = 28*A008591(n) = 36*A008589(n) = 252*A001477(n). (End)

cp's OEIS Frontend

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)).

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