A316095 Numbers n such that A(n+1) = A(n) + 3, where A() = A005101() are the abundant numbers.

231, 232, 385, 386, 544, 545, 699, 700, 858, 859, 1014, 1015, 1172, 1173, 1326, 1327, 1431, 1488, 1600, 1601, 1645, 1646, 1699, 1700, 1806, 1807, 1850, 1959, 1960, 2015, 2016, 2093, 2094, 2119, 2120, 2221, 2222, 2272, 2273, 2378, 2379, 2433, 2434, 2583, 2584

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Formula

Sequence is { n | A005101(n+1) = A005101(n) + 3 }.

Sequence is { n | A125115(n) = 3 }.

Maple

with(numtheory): A:=select(n->sigma(n)>2*n, [$1..20000]):  a:=select(j->A[j+1]=A[j]+3, [$1..nops(A)-1]);

Mathematica

Position[Map[{#1, #2 - 3} & @@ # &, Partition[Select[Range[12000], DivisorSigma[1, #] > 2 # &], 2, 1]], _?(SameQ @@ # &)][[All, 1]] (* Michael De Vlieger, Jun 29 2018 *)

Prog

(GAP) A:=Filtered([1..20000], n->Sigma(n)>2*n);;  a:=Filtered([1..Length(A)-1], i->A[i+1]=A[i]+3);
(PARI) lista(nn) = {my(va = select(x->(sigma(x) > 2*x), [1..nn]), dva = vector(#va-1, k, va[k+1] - va[k])); select(x->(x==3), dva, 1); } \\ Michel Marcus, Jul 03 2018

Crossrefs

A228382 is the main sequence for this entry.

Numbers n such that A(n+1) = A(n) + k, where A() = A005101() are the abundant numbers: A169822 (k=1), A303741 (k=2), this sequence (k=3), A316096 (k=4), A316097 (k=6).

Cf. A005101.

Sequence in context: A323321 A156742 A031965 * A345795 A088289 A046009

Adjacent sequences: A316092 A316093 A316094 * A316096 A316097 A316098

Keyword

nonn

Author

Muniru A Asiru, Jun 25 2018

Status

approved