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A130826 a(n) is the smallest number such that twice the number of divisors of (a(n)-n)/3 gives the n-th term in the first differences of the sequence produced by the Flavius Josephus sieve, A000960.

%I A130826 #16 Nov 17 2023 01:36:24
%S A130826 4,8,15,16,23,42,55,200,81,46,119,192,205,196622,12303,88,449,558,127,
%T A130826 1748,786453,58,2183,3096,1105,786458,12582939,568,2189,2730,9247,572,
%U A130826 8673,3106,2195,8676,145,110630,3819,2200,786473,20202,79,7604,7077933
%N A130826 a(n) is the smallest number such that twice the number of divisors of (a(n)-n)/3 gives the n-th term in the first differences of the sequence produced by the Flavius Josephus sieve, A000960.
%C A130826 The first six terms in the sequence are those from the TV show Lost, see A104101.
%H A130826 M. E. Andersson, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa85/aa8542.pdf">Das Flaviussche Sieb</a>, Acta Arith., 85 (1998), 301-307.
%H A130826 V. Gardiner, R. Lazarus, N. Metropolis and S. Ulam, <a href="http://www.jstor.org/stable/3029719">On certain sequences of integers defined by sieves</a>, Math. Mag., 29 (1955), 117-119.
%H A130826 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%e A130826 a(8)=200 because the 8th term in A056526 is 14. Half of that is 7. The smallest number with seven divisors is 64 and 64*3 + 8 = 200.
%Y A130826 Cf. A000960, A056526, A104101, A005179.
%K A130826 dumb,nonn
%O A130826 1,1
%A A130826 Stephen Casey (hexomino(AT)gmail.com), Jul 17 2007
%E A130826 Corrected and extended by _Alois P. Heinz_, Nov 27 2009