cp's OEIS Frontend

A316097 Numbers m such that A(m+1) = A(m) + 6, where A() = A005101() are the abundant numbers.

%I A316097 #16 Mar 01 2025 03:20:27
%S A316097 1,4,5,8,9,12,15,20,27,28,29,30,33,34,37,38,41,42,49,54,55,56,57,58,
%T A316097 61,66,67,68,73,76,77,80,84,89,92,97,98,101,102,103,108,113,116,119,
%U A316097 122,123,126,129,134,137,142,143,144,145,152,153,160,161,162,163
%N A316097 Numbers m such that A(m+1) = A(m) + 6, where A() = A005101() are the abundant numbers.
%H A316097 Amiram Eldar, <a href="/A316097/b316097.txt">Table of n, a(n) for n = 1..10000</a>
%F A316097 Sequence is { m | A005101(m+1) = A005101(m) + 6 }.
%F A316097 Sequence is { m | A125115(m) = 6 }.
%F A316097 a(n) = A091194(A316099(n)). - _Amiram Eldar_, Mar 01 2025
%p A316097 with(numtheory): A:=select(n->sigma(n)>2*n,[$1..700]):  a:=select(j->A[j+1]=A[j]+6,[$1..nops(A)-1]);
%t A316097 Position[Map[{#1, #2 - 6} & @@ # &, Partition[Select[Range[10^3], DivisorSigma[1, #] > 2 # &], 2, 1]], _?(SameQ @@ # &)][[All, 1]] (* _Michael De Vlieger_, Jun 29 2018 *)
%o A316097 (GAP) A:=Filtered([1..700],n->Sigma(n)>2*n);;  a:=Filtered([1..Length(A)-1],i->A[i+1]=A[i]+6);
%o A316097 (PARI) list(lim) = {my(k = 1, k2, m = 0); for(k2 = 2, lim, if(sigma(k2, -1) > 2, if(k2 == k1 + 6, print1(m, ", ")); m++; k1 = k2));} \\ _Amiram Eldar_, Mar 01 2025
%Y A316097 A316099 is the main sequence for this entry.
%Y A316097 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), A316096 (k=4), this sequence (k=6).
%Y A316097 Cf. A005101, A091194.
%K A316097 nonn
%O A316097 1,2
%A A316097 _Muniru A Asiru_, Jun 25 2018