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A316099 Abundant numbers that differ from the next abundant number by 6. 6
12, 24, 30, 42, 48, 60, 72, 90, 114, 120, 126, 132, 144, 150, 162, 168, 180, 186, 210, 228, 234, 240, 246, 252, 264, 282, 288, 294, 312, 324, 330, 342, 354, 372, 384, 402, 408, 420, 426, 432, 450, 468, 480, 492, 504, 510, 522, 534, 552, 564, 582, 588, 594, 600 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
From Amiram Eldar, Sep 02 2022: (Start)
All the terms are even, since all the multiples of 6 that are larger than 6 are abundant numbers.
The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 8, 85, 865, 8716, 87668, 875528, 8761027, 87606693, 875947187, ... . Apparently, the asymptotic density of this sequence exists and equals 0.087... . (End)
LINKS
EXAMPLE
12 is abundant, 13, 14, 15, 16 and 17 are deficient, 18 is abundant.
24 is abundant, 25, 26, 27, 28 and 29 are deficient, 30 is abundant.
MAPLE
with(numtheory): A:=select(n->sigma(n)>2*n, [$1..800]): a:=seq(A[i], i in select(n->A[n+1]-A[n]=6, [$1..nops(A)-1]));
MATHEMATICA
q[n_] := DivisorSigma[1, n] > 2 n; Select[Range[600], q[#] && SelectFirst[# + Range[6], q] == # + 6 &] (* Giovanni Resta, Jul 01 2018 *)
PROG
(GAP) A:=Filtered([1..800], n->Sigma(n)>2*n);; a:=List(Filtered([1..Length(A)-1], i->A[i+1]-A[i]=6), j->A[j]);
CROSSREFS
Subsequence of A005101.
Cf. A343302.
Cf. A231626, which has many common terms when 1 is subtracted.
Sequence in context: A108938 A085236 A068567 * A082801 A328587 A328632
KEYWORD
nonn
AUTHOR
Muniru A Asiru, Jun 25 2018
STATUS
approved

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Last modified May 21 02:29 EDT 2024. Contains 372720 sequences. (Running on oeis4.)