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

%I A316095 #22 Mar 01 2025 03:19:58
%S A316095 231,232,385,386,544,545,699,700,858,859,1014,1015,1172,1173,1326,
%T A316095 1327,1431,1488,1600,1601,1645,1646,1699,1700,1806,1807,1850,1959,
%U A316095 1960,2015,2016,2093,2094,2119,2120,2221,2222,2272,2273,2378,2379,2433,2434,2583,2584
%N A316095 Numbers m such that A(m+1) = A(m) + 3, where A() = A005101() are the abundant numbers.
%H A316095 Amiram Eldar, <a href="/A316095/b316095.txt">Table of n, a(n) for n = 1..10000</a>
%F A316095 Sequence is { m | A005101(m+1) = A005101(m) + 3 }.
%F A316095 Sequence is { m | A125115(m) = 3 }.
%F A316095 a(n) = A091194(A228382(n)). - _Amiram Eldar_, Mar 01 2025
%p A316095 with(numtheory): A:=select(n->sigma(n)>2*n,[$1..20000]):  a:=select(j->A[j+1]=A[j]+3,[$1..nops(A)-1]);
%t A316095 Position[Map[{#1, #2 - 3} & @@ # &, Partition[Select[Range[12000], DivisorSigma[1, #] > 2 # &], 2, 1]], _?(SameQ @@ # &)][[All, 1]] (* _Michael De Vlieger_, Jun 29 2018 *)
%o A316095 (GAP) A:=Filtered([1..20000],n->Sigma(n)>2*n);;  a:=Filtered([1..Length(A)-1],i->A[i+1]=A[i]+3);
%o A316095 (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
%Y A316095 A228382 is the main sequence for this entry.
%Y A316095 Numbers m such that A(m+1) = A(m) + k, where A() = A005101() are the abundant numbers: A169822 (k=1), A303741 (k=2), this sequence (k=3), A316096 (k=4), A316097 (k=6).
%Y A316095 Cf. A005101, A091194.
%K A316095 nonn
%O A316095 1,1
%A A316095 _Muniru A Asiru_, Jun 25 2018