cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A125115 Differences between consecutive abundant numbers.

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%I A125115 #49 Oct 21 2020 09:09:32
%S A125115 6,2,4,6,6,4,2,6,6,2,4,6,4,2,6,2,4,4,2,6,4,2,2,4,4,2,6,6,6,6,2,4,6,6,
%T A125115 4,2,6,6,2,4,6,6,4,2,2,4,4,2,6,4,2,2,4,6,6,6,6,6,2,4,6,2,4,4,2,6,6,6,
%U A125115 4,2,2,4,6,2,4,6,6,4,2,6,2
%N A125115 Differences between consecutive abundant numbers.
%C A125115 One may think that a(n) is always even and greater than 1. This is not the case as can be seen with A096399 or A228382. - _Michel Marcus_, Aug 21 2013
%H A125115 Muniru A Asiru, <a href="/A125115/b125115.txt">Table of n, a(n) for n = 1..10000</a>
%F A125115 From _Amiram Eldar_, Oct 21 2020: (Start)
%F A125115 a(n) = A005101(n+1) - A005101(n).
%F A125115 Asymptotic mean: lim_{n->oo} (1/n) Sum_{k=1..n} a(k) = 1/A302991 = 4.0384... (End)
%e A125115 a(1) = 6 because 18 - 12 = 6; a(4) = 6 because 30 - 24 = 6.
%t A125115 #[[2]] - #[[1]]&/@Partition[Select[Range[300], DivisorSigma[1, #] > 2# &], 2, 1] (* _Harvey P. Dale_, Dec 02 2006 *)
%t A125115 Differences[Select[Range[300], DivisorSigma[1, #] > 2# &]] (* _Alonso del Arte_, Apr 29 2019 *)
%o A125115 (PARI) lista(nn) = {lastab = 0; for (i=1, nn, if (sigma(i) > 2*i,if (lastab, print1(i - lastab, ", ")); lastab = i;););} \\ _Michel Marcus_, Aug 21 2013
%o A125115 (GAP) A:=Filtered([1..350],n->Sigma(n)>2*n);;  a:=List([1..Length(A)-1],i->A[i+1]-A[i]); # _Muniru A Asiru_, Jun 09 2018
%Y A125115 Cf. A005101, A096399, A228382, A302991.
%K A125115 easy,nonn
%O A125115 1,1
%A A125115 _Jason G. Wurtzel_, Nov 21 2006
%E A125115 More terms from _Michel Marcus_, Aug 21 2013