login
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
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
Subsequence of A005101.
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).
Sequence in context: A135801 A078210 A174628 * A308664 A184065 A259734
KEYWORD
nonn
AUTHOR
Muniru A Asiru, Jun 25 2018
STATUS
approved