cp's OEIS Frontend

A190612 Numbers k such that (tau(k-1) + tau(k+1))/tau(k) is an integer, where tau(k)=A000005(k).

%I A190612 #19 Oct 20 2024 02:34:38
%S A190612 6,7,11,13,19,20,23,25,28,29,31,32,34,39,41,43,46,47,51,52,53,55,56,
%T A190612 57,59,61,62,67,68,71,73,74,79,83,85,86,87,89,94,95,97,103,107,109,
%U A190612 113,119,127,129,131,133,134,137,139,141,142,149,151,152,155,157
%N A190612 Numbers k such that (tau(k-1) + tau(k+1))/tau(k) is an integer, where tau(k)=A000005(k).
%H A190612 Nathaniel Johnston, <a href="/A190612/b190612.txt">Table of n, a(n) for n = 1..10000</a>
%H A190612 Vaclav Kotesovec, <a href="/A190612/a190612.jpg">Plot of a(n)/n for n = 1..2000000</a>
%e A190612 6 is a term because (tau(5) + tau(7))/tau(6) = 1;
%e A190612 7 is a term because (tau(6) + tau(8))/tau(7) = 4;
%e A190612 11 is a term because (tau(10) + tau(12))/tau(11) = 5;
%e A190612 13 is a term because (tau(12) + tau(14))/tau(13) = 5.
%p A190612 with(numtheory): A190612 := proc(n) option remember: local k: if(n=1)then return 6:fi: for k from procname(n-1)+1 do if(tau(k-1)+tau(k+1) mod tau(k) = 0)then return k: fi: od: end: seq(A190612(n),n=1..70); # _Nathaniel Johnston_, May 14 2011
%t A190612 Select[Range[200], IntegerQ[(DivisorSigma[0, #-1] + DivisorSigma[0, #+1]) / DivisorSigma[0, #]] &] (* _Vaclav Kotesovec_, Feb 14 2019 *)
%Y A190612 Cf. A000005 (number of divisors of n), A074757, A090502.
%K A190612 nonn
%O A190612 1,1
%A A190612 _Juri-Stepan Gerasimov_, May 14 2011