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Numbers n such that A(n+1) = A(n) + 6, where A() = A005101() are the abundant numbers.
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%I #8 Aug 04 2018 14:20:57

%S 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 61,66,67,68,73,76,77,80,84,89,92,97,98,101,102,103,108,113,116,119,

%U 122,123,126,129,134,137,142,143,144,145,152,153,160,161,162,163

%N Numbers n such that A(n+1) = A(n) + 6, where A() = A005101() are the abundant numbers.

%F Sequence is { n | A005101(n+1) = A005101(n) + 6 }.

%F Sequence is { n | A125115(n) = 6 }.

%p 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 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 (GAP) A:=Filtered([1..700],n->Sigma(n)>2*n);; a:=Filtered([1..Length(A)-1],i->A[i+1]=A[i]+6);

%Y A316099 is the main sequence for this entry.

%Y Numbers n such that A(n+1) = A(n) + 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 Cf. A005101.

%K nonn

%O 1,2

%A _Muniru A Asiru_, Jun 25 2018