A316098 Abundant numbers that differ from the next abundant number by 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

Muniru A Asiru, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A316095 A316096 A316097 * A316099 A316100 A316101

Keyword

nonn

Author

Muniru A Asiru, Jun 25 2018

Status

approved