A316096 - OEIS

%I #15 Mar 01 2025 03:20:41

%S 3,6,11,13,17,18,21,24,25,32,35,40,43,46,47,50,53,60,63,64,69,72,75,

%T 78,85,88,91,94,95,100,105,106,109,112,115,117,121,124,127,130,132,

%U 136,139,140,147,148,151,154,157,159,165,168,171,176,177,180,181,184

%N Numbers m such that A(m+1) = A(m) + 4, where A() = A005101() are the abundant numbers.

%H Amiram Eldar, <a href="/A316096/b316096.txt">Table of n, a(n) for n = 1..10000</a>

%F Sequence is { m | A005101(m+1) = A005101(m) + 4 }.

%F Sequence is { m | A125115(m) = 4 }.

%F a(n) = A091194(A316098(n)). - _Amiram Eldar_, Mar 01 2025

%p with(numtheory): A:=select(n->sigma(n)>2*n,[$1..1000]):  a:=select(j->A[j+1]=A[j]+4,[$1..nops(A)-1]);

%t Position[Map[{#1, #2 - 4} & @@ # &, Partition[Select[Range[10^3], DivisorSigma[1, #] > 2 # &], 2, 1]], _?(SameQ @@ # &)][[All, 1]] (* _Michael De Vlieger_, Jun 29 2018 *)

%o (GAP) A:=Filtered([1..1000],n->Sigma(n)>2*n);;  a:=Filtered([1..Length(A)-1],i->A[i+1]=A[i]+4);

%o (PARI) list(lim) = {my(k = 1, k2, m = 0); for(k2 = 2, lim, if(sigma(k2, -1) > 2, if(k2 == k1 + 4, print1(m, ", ")); m++; k1 = k2));} \\ _Amiram Eldar_, Mar 01 2025

%Y A316098 is the main sequence for this entry.

%Y Numbers m such that A(m+1) = A(m) + k, where A() = A005101() are the abundant numbers: A169822 (k=1), A303741 (k=2), A316095 (k=3), this sequence (k=4), A316097 (k=6).

%Y Cf. A005101, A091194.

%K nonn

%O 1,1

%A _Muniru A Asiru_, Jun 25 2018