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

Author

Muniru A Asiru, Jun 25 2018

Keywords

• nonn

Examples

			20 is abundant, 21, 22 and 23 are deficient, 24 is abundant.
36 is abundant, 37, 38 and 39 are deficient, 40 is abundant.
		

Links

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

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).

Cf. A316096.

Programs

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]);

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 *)

PARI

list(lim) = {my(k = 1, k2); for(k2 = 2, lim, if(sigma(k2, -1) > 2, if(k2 == k1 + 4, print1(k1, ", ")); k1 = k2));} \\ Amiram Eldar, Mar 01 2025

Formula

a(n) = A005101(A316096(n)). - Amiram Eldar, Mar 01 2025