|
|
A316098
|
|
Abundant numbers that differ from the next abundant number by 4.
|
|
4
|
|
|
20, 36, 56, 66, 80, 84, 96, 104, 108, 140, 156, 176, 192, 200, 204, 216, 224, 260, 272, 276, 300, 308, 320, 336, 360, 368, 380, 392, 396, 416, 440, 444, 456, 464, 476, 486, 500, 516, 528, 540, 546, 560, 572, 576, 608, 612, 620, 636, 644, 650, 680, 696, 704
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
EXAMPLE
|
20 is abundant, 21, 22 and 23 are deficient, 24 is abundant.
36 is abundant, 37, 38 and 39 are deficient, 40 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]=4, [$1..nops(A)-1]));
|
|
MATHEMATICA
|
q[n_] := DivisorSigma[1, n] > 2 n; Select[Range[704], q[#] && q[# + 4] && ! q[# + 1] && ! q[# + 2] && ! q[# + 3] &] (* Giovanni Resta, Jul 01 2018 *)
SequencePosition[Table[If[DivisorSigma[1, n]>2n, 1, 0], {n, 750}], {1, 0, 0, 0, 1}][[;; , 1]] (* Harvey P. Dale, Mar 02 2023 *)
|
|
PROG
|
(GAP) A:=Filtered([1..800], n->Sigma(n)>2*n);; a:=List(Filtered([1..Length(A)-1], i->A[i+1]-A[i]=4), j->A[j]);
|
|
CROSSREFS
|
Abundant numbers that differ from the next abundant number by k: A096399 (k=1), A228382 (k=3), this sequence (k=4), A306497 (k=5), A316099 (k=6).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|