cp's OEIS Frontend

A173016 Numbers k such that the sequence B = B_k defined by {B(1) = 1; for i >= 2: B(i) = the smallest number h such that sigma(h) = A000203(h) = B(i-1) + k; or B(i) = 0 if no such number h exists} is not the sequence {A063524(j): j >= 1}.

%I A173016 #17 Mar 24 2024 12:22:54
%S A173016 1,2,3,4,5,6,7,8,11,12,13,14,15,17,18,19,20,23,24,27,28,29,30,31,32,
%T A173016 35,36,37,38,39,40,41,42,43,44,47,48,53,54,55,56,57,59,60,61,62,63,67,
%U A173016 68,71,72,73,74,77,78,79,80,83,84,89,90,91,92,93,95,96,97,98,101
%N A173016 Numbers k such that the sequence B = B_k defined by {B(1) = 1; for i >= 2: B(i) = the smallest number h such that sigma(h) = A000203(h) = B(i-1) + k; or B(i) = 0 if no such number h exists} is not the sequence {A063524(j): j >= 1}.
%C A173016 A063524(n) = characteristic function of 1 = 1,0,0,0,0,0,0,0,0,0,0,0, ...
%C A173016 Numbers k such that A051444(k) and A051444(k+1) are not simultaneously equal to 0.
%C A173016 Complement of A173015.
%H A173016 Amiram Eldar, <a href="/A173016/b173016.txt">Table of n, a(n) for n = 1..10000</a>
%e A173016 a(1) = k = 1 because a_1(n)= A000035(n) = 1,0,1,0,1,0,1,0,1,0,1,0, ...
%e A173016 a(2) = k = 2 because a_2(n)= A173012(n) = 1,2,3,0,0,0,0,0,0,0,0,0, ...
%e A173016 a(3) = k = 3 because a_3(n)= A173013(n) = 1,3,5,7,0,2,0,2,0,2,0,2, ...
%e A173016 a(3) = k = 4 because a_4(n)= A173014(n) = 1,0,3,4,7,0,3,4,7,0,3,4, ...
%t A173016 seq[max_] := Module[{t = Table[1, {max}]}, t[[Complement[Range[max], Table[ DivisorSigma[1, n], {n, 1, max}]]]] = 0; Complement[Range[max - 1], SequencePosition[t, {0, 0}][[;; , 1]]]]; seq[120] (* _Amiram Eldar_, Mar 22 2024 *)
%Y A173016 Cf. A000035, A000203, A063524, A173012, A173013, A173014, A173015.
%K A173016 nonn
%O A173016 1,2
%A A173016 _Jaroslav Krizek_, Nov 06 2010
%E A173016 Definition revised by Editors of OEIS, Mar 24 2024